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October 26, 1908— June 6, 1910. 


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The Laws of Mobility and Diffusion of the Ions formed in Gaseous Media. 

By E. M. Wellisch. (Communicated by Sir J. J. Thomson) . 1 
The Radioactivity of Rubidium. By Norman Campbell . . .11 
Jn the Free Pressure in Osmosis. By L. Vegard. (Communicated by 

Sir J. J. Thomson.) (Two figs, in Text) .... .13 

Therapeutic Inocidation for Generalised Bacterial Infections. By L. 

Noon. (Communicated by Professor G. Sims Woobhead.) (Six 

figs, in Text) 24 

In the examination of living leucocytes in vitro. By Constant Ponder. 

(Communicated by W. E. Dixon.) (Two figs, in Text) ... 30 
On the Relation between Ionization and Pressure for Rontgen Rays in 

different Gases. By J. A. Crowther. (Communicated by Sir J. J. 

Thomson.) (Two figs, in Text) 34 

On the Relative Ionization produced by Rontgen Rays in different Gases. 

By J. A. Crowther. (Communicated by Sir J. J. Thomson) . 38 
The Relationship between Hitman and Bovine Tiiberculosis. By Professor 

G. Sims Woodhead 40 

The radiation of various spectral lines of neon, heliuin and sodium in a 

magnetic field. By J. E. Purvis 45 

The transmission of Trypanosoma lewisi by fleas and lice. By Professor 

G. H. F. NUTTALL ^3 

The presence of anticoagidin in the salivary glands of Argas persicus. 

By Professor G. H. F. Nuttall 53 

The mode of action of specific substances. By W. E. Dixon and 

P. Hamill . " 54 

The action of specific substances in toxaemia. By W. E. Dixon and 

W. H. Harvey 54 

The Migration Constants of Dilute Solutions of Hydrochloric Acid. By 

C. Chittock. (Two figs, in Text) 55 

On the Carriers of the Positive Charges of Electricity emitted by hot ivires. 

By Sir J. J. Thomson 64 

viii Gontents. 

■ ■ PAGE 

An Electric Detector for Electromagnetic Waves. By E. M. Wellisch. 
(Communicated by Professor Sir J. J. Thomson.) (One fig. in. 
Text) 337. 

Aldahra and neighbouring Islands. By J. C. F. Fryer. (Plate XII) . 340 

Notes on the larger Cetacea. By D. G. Lillie. (Communicated by 

A. E. Shipley) 347 

Experimental inv.estigation as to Dependence of the Weight of a Body on 
its state of Electrification. By L. Southerns. (Communicated by 
Professor Sir J. J. Thomson.) (Five figs, in Test) . . , . . 352 

Note on an Attempt to Detect a Difference in the Magnetic Properties 
of the two hinds of Ions of Oxygen. By Miss D. B. Pearson. (Com- 
municated by Professor Sir J. J. Thomson) 373 

On the theory of the motion of charged Ions through a Gas. By Professor 

Sir J. J. Thomson 375 

On the relative velocities of diffusion in aqueous solution of rubidium and 

caesium chlorides. By G. R. Mines. (Two figs, in Text) . .381 
Note on the iise of the experimental method described in the preceding 

paper. By A. V. Hill. (One fig. in Text) 387 

A note on some fossil plants from Newfoundland. By E. A. Newell 

Arber. (Two figs, in Text) 390 

A note on Gardiocarpon compressum, Will. B}^ Mrs E. A. Newell i 

Arber. (Communicated by E. A. Newell Arber) . . . 393' 
On a oiew species of Physostoma from the Lower Carboniferous Rocks of 

Pettycur (Fife). By W. T. Gordon. (Communicated by E. A. 

Newell Arber) 395 

On the relation betioeen the fossil Osmundaceae and the Zygopterideae. 

By W. T. Gordon. (Communicated by E. A. Newell Arber) . 398 
On the occurrence of Schizoneura paradoxa, Schimper and Mougeot, in 

the Biinter of Nottingham. By R. D. Vernon. (Communicated 

by E. A. Newell Arber) 401 

Notes on the genus Schizoneura, Schimper and Mougeot. By L. J. 

Wills. (Communicated by E. A. Newell Arber) . . . 406 
On Petnfied Plant Remains from the Upper Coal Measures of Bristol. 

By D. G. Lillie. (Communicated by E. A. Newell Arber) . 411 

On the assimilating tissues of some Coal Measure Plants. By H. 

Hamshaw Thomas 413 

The production of Cathode Particles by Homogeneous Rontgen Radia- 
tions. By R. T. Beatty. (Communicated by Professor Sir J. J. 

Thomson.) (Three figs, in Text) . .416 

The solution of a system of differential equations occurring in the theory 
■ of radio-active tra)isformatio7is. By H. Bateman. (One fig. in Text) 423 

Contents. ix 


O71 double-sixes. By W. Burnside . . . . . . . . 428 

On the Procession and Pupation of the Larva of Cnethocampa pinivora. 

By T. G. Edwards. (Communicated by H. H. Brindley) . . 431 

Secondary Rontgen Rays from Metallic Salts. By J. L. Glasson. (Com- 
municated by Professor Sir J. J. Thomson.) (Five figs, in Text) . 437 

On the Transmission of ^-rays. By J. A. Crowther. (Six figs, in Text) 442 

Some Experiments on lonisation in Dried Air. By S. G. Lusby. (Com- 
municated by Professor Sir J. J. Thomson) 459 

On the Scattering of rapidly moving Electrified Particles. By Professor 

Sir J. J. Thomson 465 

Jacohi's double-residue theorem in relation to the theory of point-groups. 

By A. C. Dixon 472 

On the phosphorescence observed on the glass of vacuum tubes ivhen the 

pressure is not very low. By Professor Sir J. J. Thomson . . 482 

On the Mobilities of the Ions produced in Air by Ultra- Violet Light. By 
A. Ll. Hughes. (Communicated by Professor Sir J. J. Thomson.) 
(Four figs, in Text) 483 

On a Dissymmetry in the Emission of the Cathode Particles which are 
produced by Homogeneous Rontgen Radiations. By R. T. Beatty. 
(Communicated by Professor Sir J. J. Thomson.) (One fig. in Text) 492 

On Right- and Left- Handedness in Barley. By R. H. Compton. (One 

fig. in Text) 495 

On Accident in Heredity, tvith special reference to Right- and Left- 

Handedness. By F. J. M. Stratton and R. H. Compton . . 507 

Discontinuities in Light Emission. II. By Norman Campbell . . ,513 

The Absorption of Bromine by Lime. By W. A. R. Wilks. (Com- 
municated by Dr Fenton) ........ 526 

Note on the Reduction of Nitrosyl GhloHde. By H. 0. Jones and 

J. K. Matthews . . 529 

The development of Trypanosoma levnsi in the Rat Flea (Ceratophyllus 
fasciatus). By C. Strickland and Dr N. H. Swellengrebel. 
(Communicated by Professor Nuttall) ...... 531 

The Development of Gnomonia erythrostoina., the Cause of Cherry Leaf 

Scorch Disease. By F. T. Brooks 534 

The Absence of Living Tubercle Bacilli from some Old Tuberculous 

Lesions in Man. By Dr Louis Cobbett ..... 536 

N^ote on the Radium-content of the Waters of the Cam, Cambridge Tap 
Water and some Varieties of Charcoal. By John Satterly. (Com- 
municated by Professor Sir J. J. Thomson) 540 

The Resolution of Externally Compensated Bases into their Optically 

active components. By Professor Pope and J. Read . . . 545 

X Contents. 


The Resolution of Dihydropapaverine. By Professor Pope and C. S. 

Gibson 545 

Further studij of the Products of Chlorination of a-PicoUne. By Dr Sell 546 
Formation of uric acid derivatives. By Dr Fenton and W. A. R. Wilks 547 
The fate of uric acid in the dog. By Harold Ackroyd. (Comnuuiicatcd 

by Mr W. E. Dixon) 547 

The Adsorption of Acids hy Carbohydrates. By F. Robinson. (Coni- 

numicated by Dr Fenton) 548 

The results of Sterilisation Experiments on the Cambridge Water. By 

G. Sims Woodhead 559 

Preliminary note on the properties of easily absorbed Rontgen Radiation. 

By R. Whiddington. (Comamiiicated by Professor Sir J. J. 

Thomson.) (One fig. iu Text) 574 

Further notes on the procession of Cnethocampa pinivora. By H. H. 

Brindley. (Plates XIII, XIV) 576 

Proceedings at the Meetings held during the Session 1909 — 1910 . . 589 
Index to Vol. XV 597 


Plates I — III. To illustrate Mr Purvis' paper . 

Plates IV — IX. To illustrate Mr Orange's paper 

Plate X. To illustrate Mr Gregory's paper 

Plate XI. To illustrate Mr Purvis' paper . 

Plate XII. To illustrate Mr Fryer's paper 

Plates XIII, XIV. To illustrate Mr Brindley's paper 





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Cantkitrg^ |PPas0p]^ka:I Scrmtg. 

The Laws of Mobility and Diffusion of the Ions formed in 
Gaseous Media. By E. M. Wellisch, Emmanuel College. 
[Communicated by Sir J. J. Thomson.] 

[Head 9 November 1908.] 

The information we possess with regard to the size and 
structure of the ions formed in gases by the action of Kontgen 
*rays is almost entirely derived from a knowledge of their rates 
of diffusion and their velocities under given electric forces*. In 
order to obtain this information theoretical expressions are 
necessary for the coefficient of diffusion (D) of an ion through 
a gas and for its velocity (k) under unit electric intensity. From 
considerations based on the kinetic theory of gases Langevinf 
has shown that k and D are expressible in the forms: 

MV 3 ' 

where e denotes the charge associated with the ion, M the mass 
of the ion, L its mean free path through the gas, and V its mean 
velocity of thermal agitation. From these forms however no 
very exact information can be deduced inasmuch as the values 
of the quantities involved cannot be directly determined from 
experiment. In the present paper expressions are given for 
k and D which involve only known physical constants of the gas 
and from which, therefore, we may expect to derive reliable 
information with regard to the constitution of the ion. 

A molecule is regarded for the present purpose as a nucleus 
surrounded by a " sphere of force " of radius |s. 

* J. J. Thomson, Conduction of Electricity through Gases, 2nd edit. Art. 38. 
t Ann. de Chim. et de Phijs. vn. 28, p. 324, 1903. 

VOL. XV. PT. I. 1 

2 Mr Wellisch, The Laws of Mohility and Diffusion 

An ion is regarded as involving two distinct elements: 

(i) a mass (independent of the charge). Considering this 
element alone, let us represent the ion as a nucleus surrounded 
by a sphere of force of radius \s'. 

(ii) a charge e (electrostatic units). During motion of the 
ion through the gas the effect of this charge is (as will be shown) 
to increase the radius of the force sphere of the ion without 
altering the mass. 

A collision occurs between any two molecules when the distance 
between their centres is equal to the sum of the radii of their 
force spheres. 

As the ion moves through the gas the charge associated with 
it attracts the neutral molecules ; there results an increase in the 
mean collision frequency of the ion and consequently a diminution 
in its mean free path. 

Expression for the ionic mean free path. 

Consider the motion of an ion and a molecule regarded in the 
light of two interacting free particles. Let R denote the potential 
due to the polarisation of the molecule by the charge on the ion*, 
so that the force, taken as wholly radial, between the ion and the 

molecule is given by -j- at a distance r. Let us reduce the 

molecule to rest and consider the relative motion as the ion 
approaches it so that the velocity at infinity was U. The 
interacting forces must now be considered as being derived from 

a potential R, m denoting the mass of the molecule. 

■^ m 

The shortest distance r to which the ion and the molecule 

approach is given by the equations : 

hU = ru, 

^ ^ ^ m 

where u denotes the velocity of the ion in this position and 
b is the length of the perpendicular from the molecule to the 
rectilineal path of the ion. 
We deduce 

I 1 Mm I . 
[ 2M+m \ 

* The polarisation of the molecule by the electric field is regarded as negligible 
in comparison with that due to the ionic charge. 

of the Ions formed in Gaseous Media. 
A collision will take place if 

Mm ^., 

2 ilf + m 

where o- = fs' + -|s, the sum of the radii of the force spheres 
of the ion and molecule. 

If R = 0, i.e. if the polarisation of the molecule due to the 
ionic charge is negligible, the condition for a collision reduces 
to h ^cr, as is otherwise obvious. 

The connection between the velocity U and the mean thermal 
ionic velocity V can be deduced by the application of Maxwell's 
law of distribution of velocities. We obtain 

Hence l-j^^^^ U' = ^MV' = ^mv'; thus Ij^^U' is the 
2M + m ^ ^ 2M+m 

mean kinetic energy of the molecular motion. 

The effect of the polarisation due to the ionic charge is 
therefore, as far as collisions are concerned, to replace a^ by 


Now the mean free path of an uncharged body of the same mass 

and dimensions as the ion is given by lirna^ \/ 1 + — > , where 

n denotes the number of molecules per c.c. Hence the actual 
mean free path of the ion is L where 

L ^ = 7rn \/ 1 -^ (T-il -\ r 

V m ( mv^ 

Expression for the potential R due to the polarisation of the 
molecule by the ionic charge. 

If the molecules of a gas are polarised by an electric field 
of intensity X, the electric moment per c.c. is —j — X, where 
K denotes the dielectric constant of the gas. 

The electric moment (a) of a molecule is therefore —, X. 

The force on the molecule is /j, -y- , which is equal to 

— . -^7 . The potential is therefore given by 


4 Mr Wellisch, The Laius of Mobility and Diffusion 

_ K-l e^ 

Sttii ' r^ ' 
when the molecule is polarised by the field due to the ionic charge. 
This expression for R assumes that the polarising field is 
uniform throughout the volume of the molecule. Langevin* has 
obtained the general expression for R in the case of a spherical 
molecule and finds it to be given by a series of "which the above 
is the most important term. 

Expressions for the mobility and coefficient of diffusion of the 


Let 7] denote the coefficient of viscosity of the gas, p its 
density, p the pressure in dynes per sq. cm. and I the molecular 
mean free path. Let n^, pi, pi, K^ denote the values of n, p, p, K 
respectively corresponding to a temperature of 0° C. and a pressure 
of 760 mm. of mercury. 

The charge e carried by the ion is taken as equal to the 
charge {E) on the monovalent ion in the electrolysis of solutions. 
This equality was established from measurements of the mobility 
and rate of diflFusion of gaseous ionsf. The exact value of the 
ionic charge is not required in the present treatment inasmuch 
as e only enters in the expression n-^e = n^E, which has been shown 
from experiments in electrolysis to have the value 1'30 x 10^", 
E being measured in electrostatic units. The product n^E is 
denoted by A. 

The gas is supposed throughout to be at a temperature of 0° C, 

We have the following equations : 

7? = A nmvl 
l~^ = TT \/2 ns^ 

/-, ^ of-, ^RA T, 1/1 

L-^ = 'jr7i\/ l-\ 0-2 J 1 -I k where o" = As + ^s 

y m [ mir ] 

K-l e- 

Jtla = 

Stt?? o""' 

MV^ = mv^ (equipartition of energy) 
e = E 

* loc. cit. p. 317. 

t For the evidence in support of this equality the reader is referred to J. J. 
Thomson, Conduction of Electricity through Gasen, 2nd edit. Art. 39. 

of the Ions formed in Gaseous Media. 

p = nm 

We deduce 

When the mass and dimensions of the ion are the same as 
those of a molecule we have M = m, s' = s, and the expression for 
the mobility becomes 

p^p I 4i'7rnmv^s'^ 
This expression can be transformed into 

,.^|i+(^^ii-^r ...w. 

PiP { ^PiPi ) 

In a similar manner we obtain for the case when M=m,s' = s, 

^^,| (z,-ii,^y> w. 

P [ ^PiP^ ) 

Consider the expressions (a) and (/3) which have been found 
for the mobility and coefficient of diffusion through a gas of an 
ion regarded as a molecule carrying a charge equal to that 
associated with the monovalent ion in electrolysis. 

For a given medium K^, pi and p^ are constant; whence 
k varies inversely as p provided rj is constant. Now by Maxwell's 
law* the coefficient of viscosity of a gas is independent of its 
density ; consequently over the range of pressures for which this 
law holds good we should expect the ionic mobility to vary 
inversely as the pressure, a conclusion which has been verified 
by experiment. Similarly we should expect the coefficient of 
diffusion to vary inversely as the density over the same range. 

The expressions for k and D involve only known physical 
constants of the gas and are therefore directly comparable with 
the results of experimental observation. The results obtained 
by substituting the observed experimental values of the quantities 
involved are given in Table I. The values of the viscosity 
coefficients and of the dielectric constants have been taken from 
Landolt and Bornstein's Tables (3rd edition); the constant p^ 
was taken as 1,013,610 (dynes per sq. cm.). 

The seventh column in the table affords an indication of the 
effect on the mobility of the electric polarisation of the molecules 
by the ionic charge; it will be seen that the effect is quite 

* Vide Jeans, Dijnamical Theory of Gases, p. 252. 


6 Mr Wellisch, The Laios of Mobility and Difusion 

CO (^ CO 



t^ CO 

Ol 00 OS 
CO <M C-T 

<M CO •-! 

CO i-H CO 

o^ IX) OD 

O SiD 







1 — 1 













C-1 -* 

CO 'X) t^ ^ 
■— I O t^ b- 

db <M c-1 CO 

t^ o 
O t- 



00 CO no 























?— 1 


1— 1 

1 — 1 






1 — 1 























W Q 

;^ d 

2- w 

0» O ^o ^ 

o d o 



m d 





>~i >T, >~> ^ 

^ M ^ u 

-4J -p -tJ CS 

w w w o 

of the Ions formed in Gaseous Media. 7 

considerable. Column 8 gives the values of the mobilities under 
a potential gradient of 1 volt per cm. which would be possessed 
by a molecule carrying a charge E if there were no retarding 
effect due to this polarisation. The remaining columns give the 
values of the mobilities as deduced from expression (a) together 
with the observed experimental values of the positive and negative 
ionic mobilities ; these values correspond to a real or hypothetical 
pressure of 760 mm. of mercury. 

Unfortunately the values of K have been determined experi- 
mentally for only a very limited number of gases and vapours ; 
in consequence there do not appear in the table several vapours 
whose mobilities have been ascertained. 

Considering that we are comparing the observed values of the 
mobility with absolute values calculated from various physical 
constants of the substances the agreement is in several cases 
quite satisfactory ; however, in the case of ammonia and the 
vapours, there is a marked divergence between the calculated 
and observed values, the former values being invariably smaller. 
The values of the dielectric constants for the vapours appear to be 
inordinately large, and, in this connection, it is interesting to note 
that it is also in the case of vapours that there is a marked 
departure from Maxwell's law, K = n^, where n is the refractive 
index. The following table will serve as an illustration : 

Table II. 





































In the case of Maxwell's law the reason for the departures 
is probably the existence in the molecule of free periods with 
durations long compared with that of the incident wave period*. 
It is possible that, in the case under consideration, owing to free 
periods of long duration in the molecules of the vapours, these 

* Vide Drude, Theory of Optics, Eng. trans, p. 389. 

8 Mr Wellisch, The Laws of Mobility and Diffusion 

have not time to be completely polarised by the adjacent ionic 
charge during a collision. It is worthy of mention that the 
large values of K which have been experimentally obtained for 
ammonia aud vapours have been ascribed by some authorities 
as being partially due to traces of conductivity which they possess. 
Without dwelling further on the cause of these departures 
from the mobility law, it appears that, on the whole, the experi- 
mental values of the mobilities of the ions can be explained 
approximately on the supposition that the ion consists of a single 
molecule of the gas, with which is associated a charge equal to 
that carried by the monovalent ion in electrol3'sis. It has been 
shown from considerations based on the kinetic theory of gases 
that, irrespective of any theory as to the structure of the ion, the 
ascertained mobility values lead of necessity to the conclusion that 
the volume of the ion is in all cases greater than that of the 
corresponding gaseous molecule. The question arises : what is 
the nature of this volume ? On the one hand, if we neglect the 
influence of the charge on the mean free path of the ion, we are 
led to the conception of the ion as a cluster of molecules held 
together by forces arising from the polarisation due to the electric 
charge. On the other hand, the effect of the charge on the 
collision frequency has been shown to be equivalent to an increase 
in the molecular sphere of force such that the resultant effective 
volume is sufficient to explain approximately the observed 
mobilities. On this view the effect of the charge is to cause 
the ion itself and the neighbouring molecules to deviate from 
their rectilineal free paths; Sutherland*, by assuming such 
deviations to occur in the case of gaseous molecules by reason 
of attractive forces between them, was able to explain accurately 
the observed variation of the viscosity of gases with temperature. 
Langevinf has obtained an expression for the ionic mobility by 
using the dynamical method employed by Maxwell in the kinetic 
theory of gases ; he concluded that the experimental values of the 
mobilities lead to the necessity of regarding the ion as a cluster 
of molecules. The question as to the nature of the volume of the 
ion as determined from the experimental mobility values could be 

decided if the ratios — for the different gaseous ions were known. 

In this connection it is worthy of mention that Professor Sir J. J. 
Thomson J has recently measured this ratio for the positive ions 
formed by cathode particles in oxygen at low pressures and came 
to the conclusion that the ion consisted of a single charged oxygen 

* Phil. Blag. v. 36, p. 507, 1893. 

t Ann. de Chim. et de Phys. viii. 5, p. 270, 1905. 

t Phil. Mag. v. 16, p. 680, 1908. 

of the Ions formed in Gaseous Media. 9 

In the course of recent experiments made by the writer to 
ascertain the ionic mobilities in a series of gases and vapours 
it was found that the mobility {k) varied inversely as the pressure 
{p) over a wide range of pressures ; however, there was observed 
a tendency of the product ph to increase at low pressures in the 
case of air, nitrous oxide and carbon dioxide, and a tendency for 
it to diminish in the case of vapours, e.g. ethyl chloride, when the 
pressures approached the vapour pressure at the temperature under 
consideration. Such deviations from the law pk = constant could 
be ascribed to variations in the size of the cluster constituting the 
ion ; however, they follow readily from the expression (a) of the 
mobility if we take into account the deviations from the law of 
Maxwell which states that the coefficient of viscosity of a gas or 
vapour is independent of its density. In the case of gases it is 
known that t) tends to diminish as the pressure is reduced beyond 
a certain value*; such a diminution would, according to the theory 
here given, tend to increase the value pk. In the case of vapours 
it has been established that ?; increases rapidly as the saturated 
state is approached ; in fact, as a result of Warburg and von Babo's 
experiments on the viscosity of carbon dioxide at high pressures, 
Meyerf came to the conclusion that the experimental values above 
certain pressures could be explained only by supposing carbon 
dioxide to behave as a liquid, the density of which is practically 
independent of pressure ; an increase in the value of 17 would, 
according to expression (a), diminish the product pk, a result in 
accordance wdth experimental observation. 

In conclusion, it is of interest to note that, on the supposition 
given above as to the nature of the ion, a satisfactory agreement 
can be obtained between the calculated and observed values of the 
coefficients of diffusion of the gaseous ions. The values of these 
coefficients have been determined by Townsend;]: for four gases. 
Instead of using the ascertained expression (/3) which is really 
involved implicitly in the expression (a) of the mobility, a slightly 
different procedure is advisable. 

If D denote the coefficient of diffusion of the ion through the 
gas, and d that of a molecule through the gas, we then have from 
the preceding theory 

d I [ '^PiPi 

The nature of the agreement between the calculated and 
observed values is shown in the following table : 

* Vide Jeans, Dynamical Theory of Gases, p. 253. 
t Kinetic Theory of Gases, Eng. trans. Art. 90. 
+ Phil. Trans. A. 193, p. 129, 1900. 

10 Mr Wellisck, The Laivs of Mobility and Diffusion of the Ions. 

Table III. 







+ ! 









Calculated from Loschmidt's observations. Vide Jeans, loc. cit., p. 274. 

Mr Norman Campbell, The Radioactivity of Rubidium. 11 

The Radioactivity of Rubidium. By JSToRMAN Campbell, M.A., 
Trinity College. 

[Bead 9 November 1908.] 

1. In the first paper by Mr Wood and myself* on the radio- 
activity of the alkali elements, it was stated that rubidium as well 
as potassium was found to be radioactive, and that the rays from 
the former metal were less penetrating than those from the latter. 
Owing to the difference in the penetrating powers of the rays, the 
relative activity of the two elements can not be determined directly 
by a comparison of the total ionisation caused by the rays from 
a thick layer, but it can be determined by measurements of the 
activity of layers of varying thickness. Such measurements on 
potassium sulphate were described in a recent paperf : similar 
measurements have now been made upon rubidium sulphate. 

2. The experiments were made in a manner exactly similar 
to those on the potassium salt, and the same apparatus was used. 
The sample of rubidium sulphate used was specially prepared by 
Kahlbaum : its purity was tested by precipitation by barium 
chloride : the weight of the sulphate precipitated agreed within 
the limits of error (1 °U with that predicted from the accepted 
atomic weight of Rb. Some difficulty was experienced in obtaining 
layers of the requisite thinness and uniformity : the method 
adopted ultimately consisted in scattering the finely powdered 
salt over the surface out of a vessel of the nature of a pepper-pot. 

The following table gives the results obtained : 

Mass of salt in tray 


Mass of salt in tray 






These experimental points lie less closely on a theoretical ex- 
ponential curve than the corresponding points for the potassium 
salt : the rubidium rays are probably less homogeneous. 

Proc. Camb. Phil. Soc. xiv. 1, pp. 15 — 21. 

t Ibid. XIV. 6, pp. 557—567. 

12 Mr Norman Campbell, The Radioactivity of Rubidium. 

3. The method of calculation explained on pp. 563, 565 of 
the last paper give directly /q, the activity of an infinitely thick 

layer of the area (o-) of the tray, and the product — , where \ is 

the absorption coefficient of the material for the rays it emits, 
and p the density of the material. If a is the ionising power of 
the total radiation from 1 gramme of the material, when all that 
radiation is absorbed in air, then 

"^ P 
For rubidium metal we obtain 

a = 14-47 ± 0-365, - = 53-2 ±2-1. 
For potassium metal, using the figures given in the last paper, we 

a = 2-003 ±-0376, - = 8-23+0-1. 

It appears then that, though, for layers infinitely thick and 
containing the same proportion of the active metal, the activity 
is slightly greater for potassium than for rubidium, the intrinsic 
activity of the latter metal is at least seven times as great as that 
of the former. 

It will be noted that the statement that the penetrating 
power of the rubidium rays is considerably less than that of the 
potassium rays is confirmed. The difference is so notable that it 
may be discovered readily by covering the active layer with a sheet 
of stout paper. Such paper absorbs half of the rubidium rays, but 
not more than 5 °/^ of the potassium rays. It is clear, therefore, 
that the activities of the two elements cannot be attributed to a 
common constituent. 

Prof McLennan and Mr Kennedy* have stated that they have 
been unable to detect any activity in rubidium salts. But, since 
they have revised some of their statements concerning the activity 
of the alkali metals, it is not impossible that agreement will be 
obtained in this matter also. 

* Phil. Mag. Sept. 1908, p. 377. 

Mr Vegard, On the Free Pressure in Osmosis. 13 

On the Free Pressure in Osmosis. By L. Vegard, Cand. 
real. (Research Student at the Cavendish Laboratory), [Com- 
municated by Sir J. J. Thomson.] 

[Read 9 November 1908.] 

1. In the introduction to their paper on osmotic pressure* 
Berkeley and Hartley mention that a method for studying osmotic 
phenomena is given by the determination of what they call the 
osmotic force, and this method " depends on the determination of 
the rate at which the solvent will flow through a semipermeable 
membrane into a large quantity of solution when there is no 
pressure on the latter. A knowledge of this rate together with 
the frictional resistance will enable the osmotic force to be 
calculated in absolute units." 

The authors, however, do not enter further into the question, 
and we get from this no clear idea as to the strict definition of the 
osmotic force. 

The following paper contains some experiments done in this 
direction as well as some conclusions to be drawn from the 
experiments. The experiments consist in some determinations 
of the frictional resistance and- of velocities produced by osmosis 
when solution and solvent are exposed to the same pressure. The 
cell used is the same as used in the experiments upon osmosis 
described in an earlier paper f. 

Determination of the Frictional Resistance. 

2. The frictional resistance depends on the velocity and is 
measured by the pressure that must be applied in order to press 
the solvent through the membrane with the velocity under con- 
sideration. If pressure and velocity are denoted by Q and V 
respectively we have Q=y'(F) provided temperature is kept con- 
stant. To find this function we have simply to determine the 
velocity corresponding to different pressures. 

The measurements were made with the same osmometer as 
described in an earlier paper and the way of proceeding the same 
as used for the determination of osmotic velocities only that now 
the solution was replaced by the pure solvent. The relation 
between Q and V has been determined in two sets of measure- 

* The Earl of Berkeley and E. G. J. Hartley, Phil. Trans. Roy. Soc. 1906, 
p. 481. 

t L. Vegard, Phil. Mag. Vol. xvi. No. 92, 93, 1908. 


Mr Vegard, On the Free Pressure in Osmosis. 

ments corresponding to a considerable difference in the maximum 
electric resistance of the membrane. Before each experiment the 
cell was electrolysed after which it was placed for about thirty 
hours in distilled water in order to remove possible substances 
soluble in water. The measurements gave the following result : 

Table I. 

Experiment 1. 

Date : Middle of May. 

Electr. Eesist. 350,000 ohms at 2° C. 

Temp. 15° C. 

Experiment 2. 

Date: June 8. 

Electr. Eesist. 130,000 ohms at 7° C. 

Temp. 15-8° C. 





3'21 atm. 

7-04 „ 
14-5 „ 
26-4 „ 

39 mm. /hour 


4-33 atm. 

8-19 „ 
12-2 „ 
21-0 „ 

78 mm. /hour 

270 „ 
420 „ 

Determinations of Osmotic Velocities. 

8. The velocities were measured with the osmometer earlier 
described for some aqueous solutions of cane sugar and no pressure 
was applied on the solution. The measurements including also 
the determination of the frictional resistance in Exp. 2 were 
carried out as quickly as possible in succession and in the order 
of increasing concentrations. The membrane was not electrolysed 
between each trial. Thus it was secured that the properties of 
the membrane were kept as nearly as possible the same under the 
whole series of measurements. The results are given in the 
following table. 

The temperature was kept at 15° C. which very nearly was 
the temperature of the room. 

The velocity is here given in an arbitrary unit as the number 
of mm. which the water level in the capillary from the cell* 
changes in one hour. For the sake of comparison with other 
experiments we shall find how this unit is connected to the 
absolute unit. To find this we must know the area of the 
membrane (0) and the inner diameter (d) of the capillary. For 
the apparatus used in Cambridge 0= 17'Ocm,^ (very nearly) and 

* See description of apparatus, loc. cit. p. 248. 

Mr Vegard, On the Free Pressure in Osmosis. 


Table II. 

gr./litre 15° 




Time for observation of velocities 

Mean time 
ing to the 

mm. /hour 



June 9, 

3.23 p.m.— 4.23 p.m. 

4.25 „ —6.11 „ 

3.53 p.m. 
5.18 „ 



June 10, 

11.10 a.m.— 11.28 a.m. 

11.19 a.m. 


11.35 „ —11.45 „ 

11.40 „ 


11.45 ,, —11.51 „ 

11.48 „ 




11.51 „ —12.31 p.m. 

12.11 p.m. 


12.31 p.m.— 12.55 „ 

12.43 „ 


12.55 „ — 1.18 „ 

1.06 „ 



1.48 „ — 3.16 „ 

2.32 „ 


June 10, 

3.23 p.m. — 3.46 p.m. 

3.35 p.m. 




3.46 „ —4.14 „ 

4.00 „ 


4.14 „ —4.58 „ 

4.36 „ 



5.01 „ —5.28 „ 

5.15 „ 


June 11, 

10.22 a.m. — 10.28 a.m. 

10.25 a.m. 


10.28 ,, —10.34 „ 

10.31 „ 


10.34 „ —10.40 „ 

10.37 „ 


11.12 „ -11.35 „ 

11.24 „ 




11.35 „ —12.10 p.m. 

11.53 „ 


12.16 p.m.— 12.50 „ 

12.33 p.m. 


12.55 „ - 2.01 „ 

1.28 „ 


2.05 „ — 3.08 „ 

2.37 „ 



3.12 „ — 4.12 „ 

3.42 „ 


c^ = 0'060cm., then if the velocity in absolute and relative units 
is denoted by V and V respectively, we find 

4-61 . 10-«F= V [cm. sec.-^]; 

V can either be considered as the number of cm.^ passing each 
cra.^ in one second or as the average linear velocity of the fluid 
close to the membrane. 

16 Mr Vegard, On the Free Pressure in Osmosis. 

Discussion of the Experiments. 

4. The relation between the friction pressure and the velocity 
is represented in Fig. 1 B curve II, corresponding to Exp. 2, Table I. 
We see that as far as the observations go the points are distributed 
round a straight line. Consequently we have 

Q=AV (1) 

where J. is a constant characteristic of the membrane and the 
fluid, and dependent on the temperature. We shall call it the 
Specific Resistance of the system. 

The law for the motion through the membrane is the same as 
that for the motion of a viscous fluid through narrow tubes. This 
fact is simplest explained by assuming that the liquid also during 
the passage through the membrane maintains the character of a 
liquid. Then in points inside the tubes of the membrane the 
fluid should possess a certain hydrostatic pressure and the cause 
of the motion at each point should be found in the pressure 
gradient at the point. 

The values of the specific resistance corresponding to the two 
experiments are — using the method of least squares — found 
to be: 

Exp. 1. A= 0-0463 or A' = 1-02 . 10^^ [dyn. cm.-i sec.-^]. 

Exp. 2. A= 0-0492 or ^' = 1-OS . lO^^ 

A corresponds to the units given in the table, A' to absolute 

We see that we get nearly the same value for the specific 
resistance in the two cases and that in spite of the fact that the 
maximum electric resistance in the last experiment was not half 
of that in the first one, where the frictional resistance even is 
somewhat smaller. Thus the maximum electric resistance seems 
to give a very delicate test for the permeability of the membrane. 
When the membrane first is well formed the mechanical resistance 
against the water flow will be very little altered for very con- 
siderable changes in the maximum electric resistance. 

5. In Fig. 1 A the measurements given in Table II are 
represented by curves giving the velocity as a function of time 
reckoned from the time when the solution was brought into 
contact with the membrane. This time was not exactly observed 
so there may be a fault of a few minutes in the time of beginning. 

We see that the velocity begins with a rather large value, but 
falls very rapidly until at a certain value the curve makes a very 
sudden bend. In the case of the three lowest concentrations the 
curve assumes a horizontal direction showing that the osmosis 
has reached a steady state. In the case of the highest concen- 

Mr Vegard, On the Free Pressure in Osmosis. 


tration, however, the velocity after the sudden bend of the curve 
continues to fall. 

The condition for a steady state and the time taken for 
reaching it depend on several circumstances. A nearer study 
of this question would require a special research. I shall here 
only call attention to some circumstances which seem to have an 






















; \ 
















/ 1 



Fig. 1. 

The time depends to some extent on the dryness of the mem- 
brane at the moment when the solution is brought into contact 
with it. Thus the membrane in the second experiment, Table II, 
was dried with filter paper while in the third the membrane was 
just so wet as to give a regular reflection of light. The result 
was that the steady state occurred much sooner in the third 
experiment and that in spite of the fact that the concentration 
was greater. 

The steady state sets in more suddenly and is better marked 
for dilute solutions than for more concentrated. We shall later 
come back to this question. Further the steady state is better 
marked and more suddenly obtained when the membrane is more 
perfect. So e.g. in the measurements described in the earlier 
paper, where the maximum resistance was much greater, the 
stationary state in all cases was reached within half-an-hour. For 

VOL. XV. PT. I. 2 

18 Mr Vegard, On the Free Pressure in Osmosis. 

the sake of comparison the curve for experiment II* is put upon 
Fig. 1 A as a dotted line. 

The power of giving a well-marked steady state after this first 
sudden bend of the curve is a quality that does not belong to any 
membrane showing osmotic activity. Even for the system here 
under consideration it appears to be a matter of degree just as 
the power of giving a reversion pressure near to the osmotic 
pressure is a power only possessed by the very best membranes. 
It will surely be of great interest to see how the different systems 
behave in this respect. 

6. When the steady state is well defined the velocity correspond- 
ing to this state can be considered as a function of concentration, 
temperature, and further of some quantities dependent on the 
membrane and the fluid. Instead of concentration we can 
introduce the osmotic pressure ttq. As long as the properties of 
the membrane and the temperature can be considered as con- 
stants we are led to consider the variation of the velocity Xq with 
the osmotic pressure of the solution. The relation between ttq 
and Xfl is represented in Fig. 2 B, curve I. On the same figure is 
also drawn the curve giving the relation between the velocity and 
the friction pressure (curve II). 

We see that curves I and II stand in a very characteristic 
relation to each other. The friction line is a tangent to the curve 
at the zero point. 

A line parallel to the tto axis cuts the curves in two points 
(ttq Xo) s^nd (QXo) which we shall call corresponding points, then 
Q is the pressure necessary to force the pure solvent through the 
membrane with a velocity equal to the osmotic velocity Xq called 
forth by a solution of osmotic pressure ttq. In general we have 

for corresponding points -< 1, and - will decrease for increasing 

velocities ; but when the velocity decreases towards zero we get 



ini(^ =1 (2). 

=0 \^o/ 

Let Q, TTo, Xo be values belonging to corresponding points. 

TT — Q . 
If we calculate the quantity " for different values of Xq 

we find that it gives a constant value. Remembering that Q = AXq 
we get the following simple equation for the curve 

- ^^» =^X^-A^ (3). 

" "X "" "X —"X 


* L. Vegard, loc, cit. p. 404, 

Mr Vegard, On the Free Pressure in Osmosis. 


The curve is determined hj two parameters A and X^. Of 
these it is only the first one for which we have a physical inter- 
pretation. As regards X^ we see from the equation that when \q 
approaches X^,, ttq approaches iiifinity. Thus X^n is the upper limit 
for the osmotic velocity in the stationary state. As to its physical 
interpretation it will depend on A, further it must depend 
on the coefficient of diffusion for cane sugar in water ; for it is 
evident as the velocity is to be produced by the action of the 
solution the velocity must be so small that the solution is able to 
maintain a certain concentration in the layer next to the mem- 

Some values of X^ calculated for a series of velocities from the 
curve directly observed are given in the following table. 



100 mm./hour 

200 „ 


350 „ 

470 mm. /hour 
430 „ 
463 „ 

480 „ 

Mean value 461 mm./hour = 2-13. 10~®[cm. sec.~^]. 

7. From the very intimate relation between the friction line 
and the velocity curve we can draw some important conclusions as 
regards the mechanism of osmotic flow. 

The work (a) required in unit time for pressing the water 
through the membrane with a velocity Xq is 

a = kQXq, 

where « is a constant dependent on the units. In the case of 
osmosis we must be able to assume that in order to bring the 
water through with a velocity Xq an amount of energy (a') is 
required which cannot be less than the energy required for 
pressing pure water through with the same velocity. Then we 
must have 

a' 5 a. 
But on the other hand the maximum of energy E which the 
system can deliver in unit time is equal to the osmotic pressure 
multiplied with the volume of solvent, which enters into the 
solution in unit time, or 

JE ^ /cttoXq. 

Now the work (a') necessary to call forth the motion of solvent 
through the membrane cannot be greater than £J, consequently 

kttqXq > a > kQXq. 


20 Mr Vegard, On the Free Pi'essure in Osmosis. 

This relation holds for all velocities. Letting \o converge towards 
zero we get 

Regarding equation (2) 

,im(-^) = 

or Lim a' = ktto'X.o = kQ\o = a= E (4). 


Thus we see that for small velocities the whole energy of the 
system is made available for the motion through the membrane and 
the work {a') required for the motion under osmosis is just the same 
as the work (a) required for pressing the pure solvent through with 
a velocity equal to the osmotic velocity. 

As the work is the same we must assume that also in the case 
of osmosis we have a motion of pure water through by far the 
greatest part of the membrane. But the motion of pure water 
must have its cause in the fall of hydrostatic pressure in the 
direction of the motion just sufficient to counteract the friction 
corresponding to the osmotic velocity. 

8. From this we are led to consider the variation of hydro- 
static pressure through the membrane. In those cases where 
there is a layer next to the solvent where there is only pure 
solvent we shall in this layer have a fall of pressure in the 
direction of the motion, and when the pressure on the solution is 
less than the corrected reversion pressure (tto')* we find that if we 
pass through the membrane from the side of the solvent the 
hydrostatic pressure will first fall to a minimum value and then 
increase to the pressure of the solution. In the latter part the 
motion takes place against the pressure fall and cannot be a 
motion of the fluid in bulk, but is an intra-molecular motion 
maintained by the energy made available when the two liquids 
are brought into contact. 

The difference between the pressure on the solvent and the 
minimum pressure we shall call the free pressure of osmosis. 
The general features for the variation of hydrostatic pressure 
through the membrane is indicated in Fig. 2. AF-^, AF^ etc. 
represent the free pressure. 

If the distance from the minimum point to the surface next to 
the solution is nl, where I is the average thickness of the mem- 
brane, then an approximate value for the free pressure q is given 
by the equation 

q = (n — l)A\. 

* See L. Vegard, loc. cit. p. 264. 

Mr Vegard, On the Free Pressure in Osmosis. 


The pressure gradient is y A, and if we knew I this could be 

found ; but at all events we see that as far as -j can be considered 

constant X would give a relative measure for the pressure gradient 
near the solvent surface. In the case where w is a very small 
quantity we get 

q = A\ = Friction Pressure (5). 

So/{/ tcon- 

Fig. 2. 


In the case of our system we have seen that for small velocities 
wis very small and the free pressure is determined by equation (5). 
Regarding equation (2) we further see that for small velocities the 
free pressure is equal to the osmotic pressure. 

9. In order to explain the properties shown by the osmotic 
velocity we are led to assume that also in the case of higher 
concentrations the quantity n will be very small in all those cases 

22 Mr Vegard, On the Free Pressure in Osmosis. 

where the stationary state is well marked. We shall here mention 
some reasons that strongly support this view. 

(1) The velocities for higher concentrations are connected to 
those for lower with a very simple function, which naturally must 
support the assumption of a similar mechanism. 

(2) The form of the curve in the case when the stationary 
state is not obtained shows clearly that the first sudden diminution 
of the velocity has a cause independent of that which causes 
the diminution after the sudden bend. The first diminution is 
naturally explained by the fact that the concentration next to the 
membrane is diminished on account of the flow of solvent, the 
latter is naturally explained by assuming that the solution on 
account of the high free pressure and of want of seraipermeability 
is gradually forced into the membrane ; for then the path along 
which the motion takes place as a diffusion will be augmented 
and the velocity diminished. From this point of view it seems to 
be a necessary condition for the forming of a well marked steady 
state that n maintain a small value. 

(3) Another support for our assumption we get by comparing 
the velocities here found with the velocities corresponding to 
TT = given in the earlier paper*. In spite of the great diiference 
in the maximum electric resistance of the membrane all the 
velocities very nearly give the same curve. On the other hand 
we saw that the frictional resistance kept very nearly constant 
from one experiment to another. Now the value of n, however 
great or small it is, must depend on the degree of semipermeability 
or upon the maximum electric resistance. If then n had a con- 
siderable value, we should expect that the velocity in the stationary 
state should vary greatly with the electric resistance, this being 
not the case we must assume n to be a small quantity. 

10. As long as w is a small quantity the free pressure is 
determined by equation (5) and we get the following rule : 

Let {q\) and (ttq \o) be corresponding points, then q is the Free 
Pressure developed in the stationary state of osmosis with a solution 
of Osmotic Pressure ttq. 

The highest free pressure in the steady state will be A\n, 
which in the case considered is only 23*3 atmospheres. 

When n is small in the steady state it must be the more so 
before this state is reached and even when the stationary state is 
not well defined we must be able to assume that n is very small 
at least at the moment the velocity sets in. In the case of the 
highest concentration the free pressure at the beginning of osmosis 
has a value of about 40 atmospheres. 

As the free pressure cannot be greater than the osmotic 

TT jA. 

pressure the possible velocities must lie between -p and — where 
* loc. cit., Exp. I, II, III. 

Mr. Vegard, On the Free Pressure in Osmosis. 23 

TTo is the osmotic pressure and q the corresponding free pressure in 
the steady state. From equation (3) follows Lim ( ° " ) = 0. 

Ao=0 V_ -A A,o / 

This gives an explanation to the fact that the osmosis for small 
concentrations immediately assumes a velocity very near to that of 
the steady state. 

11. When the pressure on the solution is augmented, the 
properties are no longer so simple as they are when tt = 0. The 
degree of semipermeability begins to play a more important part 
as regards the velocity. As stated in the earlier paper the 
absolute value of the velocity for pressures less than the reversion 
pressure and when other circumstances are the same is greater 
for a more perfect membrane. The increase of pressure was 
accompanied by a sudden decrease in the velocity, and this 
decrease is the greater the less perfect the membrane is. If the 
membrane was quite stable for pressures and quite semipermeable 
we should expect that an increase of the pressure on the solution 
with an amount tt would have the same effect on the velocity as 
if the concentration was diminished to a value G corresponding to 
an osmotic pressure ttq — tt. As a consequence of this the velocity 
curve in the interval < tt < ttq would be 

TTo — TT = r- 

where A and X,^ should have the same values as before if we 
assume the qualities of the membrane and the temperature to be 
the same. The direction of the tangent at the reversion point 
should be that of the friction line. In general we find at this point 

-J— >A, only if the characteristic point lies near to the reversion 

point we find -j- nearly equal to A. This seems to be a special 

case of the more general rule that the direction of the velocity 
curve* just before reaching the characteristic point at least for 
more perfect membranes is very near to that of the friction line 
corresponding to the same membrane and temperature. 

12, From the preceding considerations we see that the experi- 
ments are very well explained by the assumption of a hydrostatic 
pressure inside the membrane which leads to the theory of the 
Free Pressure. This theory, however, gives no explanation of the 
manner in which the semipermeability is brought about in the 
layer next to the solution. The effect of the membrane is 
equivalent to a very great resistance against the flow of solution 
in bulk whatever .may be the manner in which this resistance is 
brought about. 

* See L. Vegard, loc. cit., Exp. I, II, III. 

24 Mr Noon, Therapeutic Inoculation for 

Therapeutic Inoculation for Generalised Bacterial Infections. 

By L. Noon, B.C., F.B.C.S., John Lucas Walker Student of 

Pathology in the University of Cambridge. [Communicated by 
Professor Woodhead.] 

[Bead 23 l^ovember 1908.] 

It will be conceded that recovery from a generalised bacterial 
infection depends on the defence-mechanism of the patient being 
called into action. To an invasion of bacteria Nature replies with 
a reaction which has for its object the increase of the natural 
defences. Since, however, this reaction often fails, it is the 
business of the medical man to ask whether Art may not improve 
on Nature in this respect. If the natural reaction is delayed or 
incomplete, that is, if it is not the best, the most efficient reaction 
of which the patient is capable, we had better seek to improve 
matters by the use of an appropriate stimulus. 

The following experiments are directed to shew that the 
presence of large numbers of infecting organisms throughout the 
system is not generally a sufficient stimulus to set the protective 
mechanism of the tissues into action at once ; while on the other 
hand a subcutaneous injection of a suitable dose of the killed* 
bacteria provides a generally efficient stimulus. 

The organism used was the B. pseudotuberculosis rodentium. 
When this was injected into the peritoneal cavity of a rabbit or 
guinea-pig there followed a general peritonitis, associated with the 
formation of miliary abscesses in the liver and spleen, and in 
guinea-pigs also in the lungs. The abdominal lymphatic glands, 
as also frequently the mediastinal glands, become caseous. At 
death the blood was found to give a pure culture of the organism 
in every case. The bacillus is nearly related to that of plague 
{B. pestis). The disease is nearly always fatal in guinea-pigs ; of 
rabbits, which received an infecting dose of -^^ of a 24 hours' agar 
slope culture, nearly one half died. 

The disease is therefore a severe one, and widely spread in the 
body of the experimental animal. The natural defensive reaction 
against this disease consists first of an increase of opsonine. 
Later on an agglutinin appears, but no bactericidal or antitoxic 
substances can be demonstrated satisfactorily. 

I traced the evolution of opsonic resistance in rabbits which 
had been infected as described above, and I found at once that a 
period of inertia follows on the infection. During this period the 

* The killed organisms referred to in this paper were subjected to a temperature 
of 60° C. for half au hour. 

Generalised Bacterial Infections. 25 

disease progresses while the defensive mechanism makes no 
answering effort. There is no considerable rise in the opsonic 
index of the blood for the first five days of the disease (Fig. 2). 
This phenomenon was observed in nine rabbits, none gave a con- 
trary result. Three of the rabbits died at the end of this critical 
period. In those which survived, the opsonic index usually rose 
rapidly, and recovery set in. In guinea-pigs a similar period of 
inertia was observed, most of the animals died about the fifth 
day, a few lived longer and shewed a rise in the opsonic index, but 
only one recovered. 

Fig. 1 gives the opsonic histories of a batch of ten guinea- 
pigs, which were all infected with similar doses on the same day, 
and which have been arranged in three groups according to the 
length of time during which they survived an infection. It is 
seen that the three guinea-pigs which lived longest had shewn 
high indices previous to their infection, and also shewed a capa- 
bility to produce a relatively large increase in opsonine in response 
to the disease. The animals which died earlier were those with a 
past history of medium or low indices. Their indices remained 
low during the disease. 

From the above it is clear that the natural reaction to the disease 
is delayed so late, that many rabbits and most guinea-pigs may be 
said to die without a struggle. An injection of killed bacilli 
beneath the skin of a normal rabbit is followed by a very different 
sequence of events (Fig. 2). In this case the animal responds to 
the stimulus with a prompt increase of opsonine, which reaches 
about double the initial value within 48 hours. The same result 
was obtained with five rabbits which were given various doses 
between 5000 million and 80,000 million killed bacilli per kilo- 
gramme of body weight. A smaller dose evoked a doubtful 
response or none at all. A similar contrast between the diseased 
and inoculated rabbits, also appeared with regard to the formation 
of agglutinin (Fig. 3). Five rabbits which were inoculated with 
killed bacilli, all had strongly agglutinating sera on the fifth day. 
Three diseased rabbits, which were tested, produced agglutinating 
sera first on the ninth day, and even then the observed agglutinating 
power was relatively small. 

It cannot be held that, in disease, the protective mechanism 
is held in check by an inhibitory influence. If a normal rabbit 
responds readily to a subcutaneous inoculation, a diseased rabbit 
responds still more readily to such a stimulus, as is shewn on 
Fig, 4. After a dose of 250 million dead bacilli per kilogramme 
of body weight on the fourteenth day of the disease, the opsonic 
index of rabbit 10 rose from 1*5 to 2"5 within 24 hours. In dealing 
with diseased animals, however, the dose of vaccine must be care- 
fully regulated. An excessive dose produces an irregular reaction 
(Figs. 5 and 6). 

26 Mr Noon, Therapeutic Inoculation for 


The presence of a generalised bacterial infection is not an 
efficient stimulus to call forth the best protective reaction of which 
an experimental animal is capable. 

Description of Figures, 

Fig. 1. Curve I, mean of opsonic indices of three guinea-pigs 
which survived infection more than 12 days (one recovered). 

Curve II, mean of indices of six guinea-pigs which survived from 
6 to 10 days. 

Curve III, index of guinea-pig which survived 5 days. 

(a) Date on which all the guinea-pigs were infected with equal 
small doses of B. pseudotuberculosis, intraperitoneally. 

(6) One guinea-pig died. 

(c) Four died. 

\d) Two died. 

The first dot of each curve represents two separate estimations of 
the index of each guinea-pig. 

Fig. 2. Continuous line, composite curve of opsonic indices of 
nine rabbits which were infected with living bacilli on day 1. 

(a) Three of these animals died. 

Interrupted line, composite curve of indices of five rabbits, inocula- 
ted with killed bacilli on day 1. 

Fig. 3. Agglutinating power of rabbits of Fig. 2, 
Continuous line, diseased rabbits (three animals). 
Interrupted line, inoculated animals. 

The numbers at the bottom refer to the same days as those in 
Fig. 2. 

Fig. 4. Opsonic index of rabbit which received a subcutaneous 
dose of 250 million killed bacilli per kilogramme of body weight on the 
14th day of the disease (a). 

The dots represent independent estimations, the curve is drawn 
through the mean of each pair of estimations. 

Fig. 5. Opsonic index of a diseased rabbit which received a sub- 
cutaneous dose of 5000 million killed bacilli per kilogramme of body 
weight. Pairs of independent estimations. 

Fig. 6. Opsonic index of the rabbit of Fig. 5, after receiving a 
subcutaneous dose of 500 million killed bacilli per kilogramme of body 
weight (a). Pairs of independent estimations. 

Generalised Bacterial Infections. 


Fig. 1. 

Fig. 2. 

28 Mr Noon, Therapeutic Inoculation for 

^ 'S^ 

Fig. 3. 

Fig. 4. 

Generalised Bacterial Infections, 


Fig. 5. 

Fig. 6. 

30 Mr Ponder, On the examination of 

On the examination of living leucocytes in vitro. By Constant 
Ponder, M.A., Emmanuel College. [Communicated by 
Mr W. E. Dixon.] 

[Bead 23 November 1908.] 

The satisfactory examination of living leucocytes has presented 
many technical difficulties. Methods have been mainly employed 
whereby the movements, and escape of the leucocytes from blood 
vessels, have been observed in the tissues of a living animal, or 
the leucocytes have been obtained, in the fluid from serous 
cavities, abscesses, or blisters, and studied in suspension, in a 
" hanging drop." It is possible to obtain a fairly clean pre- 
paration by centrifugalizing citrated blood, as in Wright's opsonic 
method, and by the usual laboratory process, in which a thin film 
of blood, prevented from drying, is examined on a warm stage ; 
a few white cells can be found, but their appearance is much 
masked by the presence of the red cells. 

The method which I am going to describe gives a perfectly 
clean preparation of a great quantity of leucocytes obtained direct 
from any blood ; the leucocytes can be kept alive for some time, in 
order that their movements and other physical properties can be 
studied, while the manipulations are so simple that they may be 
carried out by a class of students. I believe, moreover, that the 
method may be useful in research work on these most important 
cells, for it is also possible in this process to allow leucocytes free 
movement for some hours, in relation to extraneous substances 
introduced in their midst, in other words to study their chemiotaxis 
" in vitro," or again, one can actually watch their behaviour, when 
moving amongst a suspension of bacteria. One can also suggest 
the interest of observing the behaviour of pathological cells, such 
as those obtained from the blood of a patient suffering from one 
of the severe anaemias. 

The method. The necessary apparatus is to be found in all 
pathological and physiological laboratories, the only unusual 
material needed is modelling clay or " Plasticine," which can be 
obtained anywhere. 

The essential point is the preparation of a blood-chamber, 
whereby the white cells are allowed to escape from the clot and 
adhere to the surface of a slide, or coverslip, the clot being 
afterwards removed. 

To make this chamber a morsel of plasticine, half the size of 
a pea, is rolled out until it is as thin as the lead of a pencil and 
about an inch and a half long ; this is then taken and gently 

living leucocytes in vitro. 


fixed on a clean slide, so as to wall in a small chamber, with an 
entrance passage leading into it, thus : 

A drop of blood is allowed to fall into the chamber at A, 
a coverslip is superimposed and gently pressed down with a glass 
slide, so that as the plasticine is flattened, blood and air are driven 
out of the passage B, which must be kept patent, so that the 
chamber is completely filled with an even layer of blood, thus : 

This needs a little practice to perform successfully, but under 
the usual circumstances, a small air bubble in the chamber does 
no harm. 

The chamber is now incubated, at about blood temperature, 
for any length of time, from ten minutes to three or four hours, 
according to requirements. 

For a class of students a very simple arrangement, doing away 
with the need for an incubator, is as follows. A warm stage is 
prepared under a microscope, by means of a copper strip, one 
end of which, resting on the microscope stage, is kept at blood 
temperature (the melting point of a fragment of cocoa butter can 
be used as a rough indicator), when the other end is heated by a 
very small flame ; on the end above the flame, a flat white dish, 
filled with normal ('75 °/^) saline solution, is placed, at a point on 
the copper (easily found by experiment) where the saline solution 
also keeps warm at a temperature of 38° C, or a little below. 
The whole slide, on which the chamber has been prepared, is 
immersed in the dish of saline, at blood temperature, and so 
incubated for at least ten minutes. 

During the period of incubation the blood clots and the 
leucocytes escape and adhere firmly in hundreds to the surface 

32 Mr Ponder, On the examination of 

of the slide and coverslip, which form the glass floor and roof of 
the blood-chamber ; it is now only necessary to clean away the 
clot. To do this, the coverslip is removed while under the surface 
of the warm saline solution by passing beneath it the point of a 
knife or needle, and what remains of the clot and plasticine is 
scraped away from the slide with a small knife. The slide should 
now be well washed in the warm saline until all free red cells 
have been rinsed off; this is shown to have taken place completely 
by the disappearance of any reddish colour, and on holding up the 
slide to the light a grey film can be seen, which consists entirely 
of leucocytes, adhering to the surface of the slide. 

If now only a temporary preparation is needed, it is merely 
necessary to take the slide out of the warm saline bath, super- 
impose a coverslip, taking care that plenty of saline lies beneath 
it, and examine it on the warm stage under the microscope. If, 
however, the preparation is to be kept some time, or it is desired 
to bring in contact with the leucocytes some other fluid such as 
serum, containing a suspension of bacteria, it is necessary to 
construct on a coverslip, a plasticine chamber, similar to the one 
originally described for obtaining the leucocytes — though in this 
case with walls made as thin as possible — and having carefully 
filled this with a large drop of the saline, or fluid, with which it is 
desired to bring the leucocytes in contact, to press the slide down 
on it, so that the chamber is completely filled with the fluid, and 
the leucocytes on the surface of the glass become situated on its 

As an alternative preparation, the coverslip of the original 
blood-chamber which is also covered with leucocytes, may be 
taken, cleaned as described above, and pressed down similarly on 
a chamber (made this time on a slide) which contains a drop of 
saline or the fluid with which it is desired that the leucocytes 
shall come in contact ; the leucocytes in this case are on the 
under surface of the coverslip, so that the preparation resembles 
that of a " hanging drop." 

The actions of the leucocytes can by this method be studied in 
two ways. Firstly, they may be allowed to live and move in the 
primary blood-chamber for some hours, the preparation being kept 
in an incubator (evaporation does not take place, as the blood dries 
across the narrow entrance and seals it), and then, when it has 
been cleaned, fixed, and stained, the positions the leucocytes have 
taken up, with regard to any foreign substance, can be observed. 
Secondly, if the primary preparation is only incubated for ten 
minutes, and the leucocytes are then transferred to a second 
chamber, we have a means whereby their movements and inter- 
actions with foreign substances can take place while under 

living leucocytes in vitro. 33 

Throughout this process the question of temperature is of some 
importance ; it is advisable that the slide to which the leucocytes 
are adherent should be kept at a temperature not much below that 
of the blood, otherwise the cells become circular and are liable to 
be washed off; on the other hand, if the preparation is heated much 
over 40° C, the leucocytes become disintegrated and disappear. 

I have found that the leucocytes will continue their movements 
for about three or four hours in the primary chamber, or for about 
an hour in the secondary; this is probably to be explained by the 
fact that the COg tension becomes so high as to terminate their 
existence sooner when the red blood cells have been removed. 

VOL. XV. PT. I. 

34 Mr Crowther, On the Relation between Ionization and 

On the Relation between Ionization and Pressure for Rontgen 
Rays in different Gases. By J. A. Crowther, B.A., St John's 
College. [Communicated by Sir J. J. Thomson,] 

[Read 23 November 1908.] 

1. In the absence of any secondary radiation, the amount of 
ionization per cubic centimetre produced in a given gas by the 
passage of Rontgen rays of given type and intensity should be 
proportional to the mass of the gas present per cubic cm. ; that is, 
if the temperature is constant, to the pressure of the gas. Thus 
in the absence of any secondary radiation, the ionization-pressure 
curve should be a straight line passing through the origin. 

If, however, the action of the rays on the gas generates 
secondary rays, this will no longer be the case. 

It was shewn in a previous paper* that in the cases of air and 
carbon dioxide, the energy of the penetrating secondary radiation 
is simply proportional to the pressure of the gas, and this result 
has subsequently been confirmed for the more powerful radiators. 

Since this type of radiation is sufficiently penetrating to pass 
through the whole of the gas between the electrodes in the 
apparatus employed, the ionization produced by it will be pro- 
portional to the intensity of the secondary radiation and to the 
pressure of the gas ; that is, to the square of the pressure of the 
gas. The ionization-pressure curve should thus have the form 


where / is the ionization and p the pressure. For most gases 
at the pressures employed in the present experiments the 
energy of this secondary radiation is too small to make any 
appreciable alteration in the shape of the curve. Taking Barkla's 
value ('00024 times the primary) for the energy of secondary 
radiation from a cubic cm, of air as being approximately correct, 
it can be shewn that in the case of the most efficient radiator 
used, namely ethyl bromide, the energy of secondary radiation at 
a pressure of 160 mm, of mercury is only about 3 °l^ of that of the 
primary beam; or since the secondary radiation is in this case 
about three times as absorbable as the primary, the secondary 
ionization should be about 9 °/^ of that produced by the primary 
rays at the pressure named. Since ethyl bromide gives off more 
than five times as much secondary radiation as methyl iodide, and 
two hundred times as much as air, it is evident that the ionization 
produced by the penetrating secondary rays in these gases is 

* Crowther, Phil. Mag. xiv. Nov. 1907, p. 653. 

Pressure for Rontgen Rays in different Gases. 


It should, however, be quite perceptible in the ionization 
pressure curve for ethyl bromide, and on turning to Fig. 1 it will 
be seen that this is the case. 

The curve for ethyl bromide, unlike those obtained for other 
gases, has a distinct upward tendency, and from the magnitude of 
its departure from the tangent through the origin, it is easy to 
deduce that, at a pressure of 160 mm., the ionization due to the 
secondary rays is about 16 °/^ of that due to the primary. 

For the other gases tried the curves shew that the effect of 
the penetrating secondary rays may be neglected. 

CzHsBr / 










\ ^ 


/ / 


/ / 



/ / 


, O 

/ / 



/ / 



/ /^ 






b K 

n ir 

in 1 

^r\ or 


Fig. 1. 


2. It was thought possible that in addition to the penetrating 
secondary rays there might be some soft secondary radiation 
(possibly soft yS-rays) emitted by the gas under the action of the 
Rontgen rays. It was with the special object of investigating 
this point that the present experiments were undertaken. It can 
easily be seen that if the pressure of the gas is so low that the 
soft secondary rays from the gas are not completely absorbed in 


36 Mr Crowther, On the Relation between Ionization and 

the gas before reaching the walls of the ionization chamber, the 
ionization-pressure curve as before should have the form 

I = Ap + Bp\ 

When, however, the pressure is high enough to cause the 
complete absorption in the gas of the soft secondary rays from 
the gas, the ionization produced by these secondary rays will be 
simply proportional to their energy, that is, simply proportional to 
the pressure of the gas ; and the whole ionization in the gas will 
again follow a simple pressure law. 



[j?rirhv / 





' / r 


/ L 



.^^-_— — — ^— 


Fig. 2. 




The apparatus employed consisted of a gas-tight brass box 
with an aluminium window to admit the rays ; the ionization was 
measured between a pair of parallel plates placed inside the box 
but outside the direct line of action of the primary beam, which 
was limited and defined by perforated lead screens. 

A second aluminium window at the far side of the box allowed 
the primary rays to pass out of the box, so that the amount of 

Pressure for Hontgen Rays in different Gases. 37 

absorption undergone by them could be measured. This was 
necessary in order to correct the results obtained, for the absorp- 
tion of the primary rays before reaching the electrodes, which in 
order to avoid secondary rays from the aluminium window were 
placed some considerable distance within the box. This correction 
(which varies with the pressure) has been applied to all the results 
given in this paper, A second similar chamber was filled with air, 
and used as a standard. 

3. The first experiments were made with the plates 6 cms. 
apart. These failed to give any indication of any departure from 
the simple pressure law (except, as stated above, in the case of ethyl 
bromide at the higher pressures). It was thought that this might 
be due to the distance between the plates being sufiicient to 
absorb completely any soft secondary rays emitted by the gas, 
even at the lowest pressures employed. The apparatus was then 
altered so that the distance between the plates was only 5 mm. ; 
the aperture of the primary beam being suitably reduced by 
means of lead slits to a width of about 2 mm., and the experiment 

The results obtained connecting pressure and ionization are 
given in Figures 1 and 2, Fig. 1 giving the results for com- 
paratively high pressures (up to 200 mm.) and Fig. 2 the results 
for ethyl bromide and methyl iodide at pressures below 20 mm. of 
mercury. The upward trend of the ethyl bromide curve is evident 
from Fig. 1. Apart from this all the curves are sensibly straight 
lines passing through the origin. There is thus no evidence of 
any appreciable amount of soft secondary radiation from the gas 
itself. If gases do emit these soft secondary rays they are either 
too absorbable to pass through 2^ mm. of gas (the half distance 
between the electrodes) even at the lowest pressures employed, or 
else they are too small in amount, compared with the ionization 
produced by the direct action of the primary rays, to be appreciable. 

The former hypothesis is not probable. By allowing the 
primary rays to graze one of the aluminium electrodes it was 
shewn that the soft secondary rays emitted by the aluminium 
under the action of the Rontgen rays passed through the whole 
distance between the plates without being completely absorbed 
by ethyl bromide at a pressure of 20 mm. of mercury. It seems 
probable therefore that practically the whole of the ionization is 
produced by the direct action of the primary rays. 

S8 Ml" Crowiher, On the Relative Ionization 'produced hy 

On the Relative Ionization produced by Rontgen Rays in 
different Oases. By J. A. Crowther, B.A., St John's College. 
[Communicated by Sir J. J. Thomson.] 

[Bead 23 November 1908.] 

It may be of interest to place on record the following results 
which have been obtained during the course of a series of experi- 
ments, still in progress, on the passage of Rontgen rays through 
gases. The apparatus was that described in a previous paper*. 
A beam of Rontgen rays was fired through the gas, between two 
parallel plate electrodes, care being taken to avoid any portion of 
the beam falling upon either of the electrodes. If this precaution 
is neglected very different values are obtained owing to the large 
amount of soft secondary j3 radiation given off by the electrodes 
under the action of the primary rays. 

The measurements given under the column headed "soft 
rays " were made with the softest rays which would produce any 
appreciable amount of ionization, and the aluminium window was 
made very thin (about -^ mm.) in order to cut off as little as 
possible of the soft radiation. The measurements labelled " hard 
rays " were made with the bulb as hard as it was possible to work 
it with a Rudge induction coil worked by a turbine mercury 

It has been suggested that the relative ionization would tend 
to follow a density law as the rays became harder. The results 
obtained in the present experiments do not give any indication of 
such a result. Compared with air as a standard, methyl iodide, 
methyl acetate and carbon dioxide shew a decrease as the rays 
get harder in the relative amount of ionization produced ; hj'drogen 
and ethyl bromide, on the other hand, give a distinct increase ; 
while ethyl chloride and carbon tetrachloride remain nearly 
constant. The exceedingly small value obtained for hydrogen 
with very soft rays (only 1 °/^ of that of air at the same pressure) 
is very remarkable. The increase in the case of ethyl bromide, 
the value for which for soft rays is already considerably above 
that required on a density law, may also be noticed. 

* Proc. Camb. Phil. Soc. Vol. xv. p. 34, 1908. 

Rontgen Rays in different Oases. 






C,H,C1 .... 


C^HsBr ... 

Soft rays 


Hard rays 


Relative Ionization. 

40 Professor Sims Woodhead, The Relationship between 

The Relationship between Human and Bovine Tuberculosis. 
By G. Sims Woodhead. Professor of Pathology. 

[Bead 23 November 1908.] 

Before the infective nature of tuberculosis had been demon- 
strated by modern methods there was considerable difference of 
opinion as to the specificity of the tuberculosis occurring in 
animals and in human subjects. Koch in his earlier observations 
seems to have had little doubt as to the identity of the tubercle 
bacillus in all forms of tuberculosis, though Klein at a very early 
date held that the bovine tubercle bacillus differed somewhat from 
that found in the human subject not only in its manner of growth 
and in its relation to the tissues but also in virulence. Theobald 
Smith, Dinwiddie and others as the result of a series of very 
careful observations called attention to what they believed were 
almost specific differences as regards size, mode of growth, virulence 
and chemical products, between the human and the bovine types 
of tubercle bacilli. During the time that I held the Grocers' 
Company Scholarship I was led to make a careful examination of 
the tuberculous material that fell into my hands with the view 
of obtaining some light on the subject of caseation in tubercle 
and of the relations of the various elements found in tubercle to 
the spread of the disease not only amongst human beings but 
amongst cattle. I was very early struck by the large proportion 
of cases of abdominal tuberculosis {tabes mesenterica) met with 
in extremely young children and after comparing my own observa- 
tions with those already made by Bang, Rilliet, and Barthez I was 
convinced that, in children at any rate, many of the cases of 
tuberculosis were the result of a kind of natural infection through 
the intestine. I found that in 127 cases of tuberculosis in 
children on whom I had the opportunity of making a post-mortem 
examination tubercular ulceration of the intestine was found in 
forty-three. Only one of these cases had succumbed during the 
first year after birth, but 14 died within two years and a half of 
birth, 10 between three and five years, 7 from six to seven and a 
half years, 5 from eight to ten years, and 6 between eleven and fifteen 
years. Although there was tuberculous ulceration in forty-three 
cases only, there was distinct tuberculous degeneration of the 
mesenteric glands in no fewer than 100 cases or nearly 79°/^ of 

Human and Bovine Tuberculosis. 41 

the whole. The acre at which these tubercular glands in the 
mesentery were found is significant. During the first year of life 
there were 4 cases; from one to two and a half years, 33; from 
three to five and a half years, 29 ; from six to seven and a half 
years, 12 ; from eight to ten years, 13 ; and from eleven to fifteen 
years, 9. In fourteen of these cases the mesenteric glands only 
were affected, that is no tubercle was found in any other part of 
the body. Here again more than half the cases appeared between 
two and five and a half years. Since these figures were published. 
Still, Shennan and the Royal Commissions on Tuberculosis in 
this country and in Germany have published corresponding 
statistics which in the main agree with those I have given and 
I only use my own figures because they were the factor that 
influenced, perhaps even biassed, my own conclusions. I should 
now like to point out that whilst the child is suckled by its mother, 
i.e. during the first year after birth, it is not nearly so liable to 
contract mesenteric trouble as at a later period; whilst during 
the next two periods during which children are living on mixed 
diet and, usually, are taking some milk from the cow, the number 
of cases of tuberculosis rises very rapidly. Dr B. Hubermaas 
studying tuberculosis of the breast pointed out that although 
tuberculosis is so common in young married women, tuberculosis 
of the breast is exceedingly rare. This observation has been 
fully confirmed by later observers. It may, of course, be sug- 
gested that tuberculosis is a disease of such slow development 
that even if it were conveyed from other sources than by food and 
by other channels than by the intestinal canal it would take some 
time for the disease to manifest itself, and therefore would not 
kill the child until it had reached an age beyond the first year. 
It must be remembered, however, that in my investigation a very 
careful search was made with the special object of finding tubercle 
and that therefore tuberculous disease even though it had not 
given rise to any symptoms during life would scarcely be over- 
looked. I do not wish to minimise the importance of infection by 
the tuberculous mother kissing and fondling her child, but this 
factor (except that the process is not extended over such a long 
period) is just as likely to be brought into play in the early years 
of life, as later. We should not expect to have the very sudden 
rise that we meet with if this were the only factor at work. It is 
evident, however, that after the first year a second factor comes 
in — food, in this instance milk, and so far as the reports of the 
Royal Commission on Tuberculosis have been published and from 
the reports from various laboratories there seems to be little 
doubt that tubercle bacilli in enormous numbers are often present 
in the milk that is supplied for human consumption. Quite apart 
from anything else then, I am satisfied that these statistics as to 

42 Professor Sims Woodhead, The Relationship between 

mesenteric tubercle plus the presence of the tubercle bacilli in 
such a large proportion of milk taken by these children are closely 

Let us now come to another aspect of the question. All those 
who have studied tuberculosis are satisfied that very numerous 
and very distinct species are affected by tuberculosis, and as Sir 
John McFadyean points out, we know of no single organism which 
will produce disease in more than half a dozen species and which 
affects either the human subject or cattle which does not also 
affect them both. It has of course been pointed out that the 
tubercle bacilli met with in various animals exhibit very varying 
degrees of virulence. They also differ considerably as to their 
rate and luxuriance of their growth, and it is quite possible that 
they may differ in other respects and perhaps differ very 
materially. In this, however, they resemble many of the other 
infective organisms. Washbourn and Eyre, for example, pointed 
out that- not only could they modify the virulence of the pneumo- 
coccus by passing it through rabbits and mice, but that by 
cultivating it as a saprophyte on sterile media in test tubes, they 
were able to render its growth much more luxuriant and at the 
same time to diminish its virulence, these alterations taking place 
much more rapidly in certain of the individual organisms than in 
others, as after cultivating them for some time they could separate 
from the same culture highly virulent organisms, growing slowly, 
and slightly virulent organisms, growing rapidly and luxuriantly. 
Pasteur's experiments on hydrophobia afford another example of 
increase and diminution of virulence by passage through different 
species of animals. Numerous observers have obtained similar 
results by the passage of a streptococcus through different species 
of animals; the streptococcus passed through the rabbit becoming 
more virulent for that animal and less so for the mouse, whilst a 
similar organism passed continuously through a series of mice 
acquires increased virulence for that animal, this being accompanied 
by a corresponding diminution in virulence of that organism for 
the rabbit. It is unnecessary to multiply examples. Anyone 
who will take the trouble to go through the appendix to the 
Second Interim Report of the Royal Commission on Tuberculosis 
will be very much struck by the marked differences in virulence of 
the tubercle bacilli separated from different cases and inoculated 
into animals. They will find that, speaking generally, the tubercle 
bacillus, that is what the Commission terms "dysgonic," is dis- 
tinctly more virulent than the rapidly and luxuriantly growing 
(eugonic) form. All varieties both as to growth and virulence have 
been found in the human subject, some appearing to produce 
extensive and rapidly generated lesions, others producing minimal 
lesions or, in some cases, none at all. It is known that alterations 

Human and Bovine Tuberculosis. 43 

in temperature of nutrient media, etc. may affect the bacillus of 
anthrax and render it almost inert, and that it may take some 
time and special conditions for the restoration of the original 
virulence. It is recognised too that the resistance of individuals 
of the same species may vary enormously even to the same 
organism, and that this comes out most markedly in the case of an 
organism of modified virulence. If this holds good in the case of 
the anthrax bacillus, may it not be equally true in the case of the 
bacillus tuberculosis ? 

Here we have to remember however that we have an organism 
that grows comparatively slowly. In the first instance it sets up 
localised lesions which in most cases at any rate are of slow 

A slowly growing organism and one that causes such com- 
paratively slowly developing lesions will in all probability undergo 
comparatively slow and slight modifications when it is placed in 
new environments and is subjected to new conditions. The direct 
evidence on these points is at present very small in amount and 
unsatisfactory in character. We have little evidence of a morpho- 
logical character. Pathologists have had so much to undertake in 
connection with the study of the bacillus in the tissues and in 
ordinary "culture" conditions that they have had little time or 
opportunity to devote to the changes in morphological and 
biological characters of the tubercle bacillus outside these two 
limited areas. 

The tuberculin reaction however has given us some evidence 
that the differences insisted upon by Koch and his followers are 
not specific, indeed are scarcely to be dignified by the term 
varietal, but the large field of biological and morphological inves- 
tigation that is just being broken, will I believe prove a most 
fruitful field to men trained in these branches of study, and how 
warmly their cooperation will be received it is scarcely necessary 
for me to emphasise. 

As far as can be gathered from the information now at our 
disposal, the character of the lesions set up by different varieties 
of the tubercle bacillus, the specificity of the reactions obtained 
with tuberculin derived from bacilli derived from human and 
bovine sources, the evidence slight though it be of modification of 
morphological and biological characters, and especially the more 
marked evidence of gradation of virulence in the two types as 
usually described, we are, I think, justified in assuming that some 
time or other we should be able to find links connecting even the 
distant extremes, in spite of the great difficulties encountered in 
tracing these links, difficulties that arise out of the comparatively 
slow growth of the tubercle bacillus both in culture and in the 
tissues, and the correspondingly slow development of the tuber- 
culosis induced by them. 

44 Professor Sims Woodhead, Human and Bovine Tuberculosis. 

So far as mode of growth and lesions produced in the tissues, 
size of organism, tuberculin reaction and all known characters 
give us any lead we are I think bound to maintain that the 
differences between bacilli obtained from tuberculous lesions in 
the human being and those obtained from similar lesions in 
cattle, are not specific, and that for this reason, the tubercle 
bacillus, from whatever source it may be derived, constitutes a 
distinct, and even grave, danger to any human or brute subject 
to which it may gain access and I for one should be unwilling to 
accept any responsibility for suggesting the relaxation of the 
laws dealing with any thing in which this highly infective agent 
is concerned. Indeed I would go further than this as I con- 
sider it essential that it is our duty to do all that we possibly 
can to strengthen the hands of Medical Officers of Health and 
their Inspectors in the difficult task with which they are now 

Mr Purvis, The radiation of various spectral lines of neon, etc. 45 

The radiation of various spectral lines of neon, helium and 
sodium in a magnetic field. By J. E. Purvis, M.A., St John's 

[Read 23 November 1908.] 

Neon. The author had already photographed the principal 
lines of neon vibrating in a magnetic field, when a paper by 
Lohmann appeared giving a short account of the effect on the 
lines when observed by means of an echelon spectroscope* : and 
since then, Lohmann has completed the measurements f. He used 
an echelon of 32 plates, the thickness of each plate being 1 cm., 
and the strength of the magnetic field was usually 11,000 units. 
He states he was able to see and to photograph the lines divided 
into 9, 12 and 15 constituents. 

Field strengths were used in the author's experiments of 26,100 
and 24,000 units respectively, as the distances between the poles 
of the magnet had to be adjusted to the diameters of the neon 
tubes. In the first series of experiments, the first order of 
Professor Liveing's 21-foot radius grating spectroscope was used, 
and, usually, there was an exposure of 20 minutes of the photo- 
graphic plates. On examining the photographs with a low power 
microscope, the author was unable to see the more complicated 
divisions of some of the lines described by Lohmann. 

Lately, the author has repeated the experiments with an echelon 
of 18 plates, the thickness of each plate being 7 J mm. ; and using 
the same field strengths as were used in the Rowland grating 
experiments. But, when the lines were divided into more than 
three or six constituents, there was a great difficulty in distinguish- 
ing clearly between the images of other orders and the images of 
some of the constituents of the divided lines. For instance as 
regards the line 6402, described by Lohmann as giving 15 con- 
stituents, one could only be sure of five constituents ; and of the 
line 5944 divided into 12 constituents by Lohmann, four constituents 
could be distinguished, of which there were two fairly sharp ones 

"' Physik. Zeits. 7 Jahrgang, No. 22, Seite 809—811. 

t " Beitr. zur Kennt. des Zeeman-phanomens," Inaug. diss., Halle, 1907. 

46 Mr Purvis, The radiation of various spectral 

vibrating parallel to the lines of force, and two very diffuse ones 
showing doubtful signs of division and vibrating perpendicularly to 
the lines of force. The importance of this difficulty cannot be 
exaggerated ; for when the gas is vibrating in the magnetic field, 
its luminosity is greatly increased ; and the very faint images of 
other orders, not clearly visible when the gas is not vibrating in the 
field, would become better marked and clearer. The constituents 
of these images would, therefore, interfere with a clear differentia- 
tion of the constituents of any particular line under observation. 

The advantage of Lohmann's apparatus was the greater dis- 
persive power of his echelon spectroscope of 32 plates as compared 
with the one of 18 plates used in these experiments, and the 
stronger field used in the present experiments did not appear to 
compensate for the less dispersion of the echelon. So that until 
the conditions of the experiments are more equal, no exact com- 
parison of the observations can be made : and there is still the 
more important difficulty of distinguishing the real constituents 
of lines from the images of other orders. However, the distances 
have been measured of the constituents of the lines unmistakably 
divided into triplets, and, also, those of the line 6383 undoubtedly 
divided into six constituents. 

The diameters of the capillary parts of the neon tubes were 
different, so that the distances between the magnet poles had to 
be altered to accommodate them : and the strengths of the field 
were 24,000 and 26,100 units respectively. The following table 
gives the distances of the two constituents of the triplets vibrating 
perpendicular to the lines of force from the one vibrating parallel 
thereto, measured on the scale of vibration numbers, i.e. the 
number of vibrations in a path of one centimetre*. The positive 
signs denote the distances in the direction of greater wave length, 
and s and p that they vibrate perpendicular or parallel to the lines 
of force. It may be of use to workers in this kind of research to 
state that the analysing Nicol prism should be placed between the 
magnet and the quartz condensing lens when analysing the various 
constituents of a divided line ; for, if it is placed between the lens 
and the slit of the spectroscope, the rotation of the polarised 
constituents by the quartz lens produces a complete inversion of 
the images when photographs are being taken in the ultra violet 
part of the spectrum, so that the two outside constituents of a 
triplet would appear to vibrate parallel to the lines of force, and 
the middle one perpendicular thereto. It is possible that the 
abnormal polarisations of certain triplets of various elements 
which have been recorded have been produced in this way. 

* Eunge and Paschen, Sitz. d. Akad., Berlin, 1902 (1), p. 721, " Zeeman-effect 
entsprechender Serienlinien." 

lines of neon, helium and sodium in a m-agnetic field. 47 


Strength of field 
26,100 units. 

Strength of field 
24,000 units. 


r + 1,237 s 
1 p 

+ 1,126 

[ -1,226 s 



r + 0,817 s 

1 Op 

+ 0,766 

[ -0,811s 



r + 1,176 s 
i p 

+ 1,129 

[ -1,184 s 



r + 1,666 s 
i ^ P 

+ 1,544 

[ - 1,587 s 



r + 1,788 s 
i /? 

+ 1,713 

[ -1,722 s 


r + 1,249 s 

+ 1,161 


i if 

[ - 1,248 s 


The line 6383-15 is divided into six constituents, and the 
distances between corresponding constituents were measured. 


Strength of field 
26,100 units. 

Strength of field 
24,000 units. 


r + 1,804 s 
+ 0,878 s 
+ 0,878 p 

- 0,878 p 
-0,878 s 
- 1,804 s 

+ 1,656 
+ 0,812 
+ 0,812 


In order to compare these numbers with Lohmann's, the follow- 
ing table contains the values obtained when they are calculated 
in terms of the strengths of the field. 


Mr Purvis, The radiation of various spectral 





^^ - 101-^ 

^^ - 10^^ 

\2x 26,100' • 

\2x 24,000' • 


r - 4,73 s 

\ ^ P 
[ + 4,69 s 


+ 4,68 


+ 4,70 


r -3,12 s 
[ + 3,10 s 


+ 3,28 


+ 3,13 


r - 4,50 s 

\ ^ p 

+ 4,53 s 


+ 4,72 


+ 4,40 


-6,38 s 


+ 6,07 s 


+ 6,32 


+ 6,07 


- 6,84 s 


+ 6,59 s 


+ 7,05 


+ 6,80 


' - 4,78 s 


+ 4,78 s 


+ 4,97 


+ 4,74 


r -6,91s 
-3,36 s 

+ 3,36j9 
+ 3,36 s 
+ 6,91 s 


+ 3,38 
+ 3,38 
+ 6,90 


+ 3,38 
+ 3,38 
+ 6,63 

The agreement between these numbers is moderately close; 
the chief differences being the two outermost constituents of the 
sextet from 6383 ; although the numbers obtained from both my 
measurements are fairly comparable. Also, there is no very close 
agreement between the numbers obtained from the triplet of 6163, 
except that the numbers obtained from my own measurements 
are comparable. 

Lohmann did not appear to observe if there were any shift of 
the lines towards the red end of the spectrum when the neon was 
vibrating in the magnetic field. It would be difficult to do this 
with an echelon, for it would be necessary to move the photo- 
graphic plate and there would be a consequent source of error. 
But, with this object in view, some photographs were taken by 

lines of neon, helium and sodium in a magnetic field. 49 

the author with the Rowland grating. To accomplish this, a 
copper slide was attached to the slit of the spectroscope, and slotted 
in such a way that, in one position, the upper half of the image was ' 
cut off during the normal vibrations of the gas, and, in another 
position, the lower half was cut off when the vibrations were under 
the influence of the magnetic field. No other alteration was made ; 
the position of the photographic plate was not altered ; the neon 
tube was not touched; and the discharge through the gas was 
exactly the same in both series of experiments. The two images 
were consequently photographed directly over each other ; and the 
following table contains the numbers, in thousandths of an 

Angstrom unit, of the shift towards the red end of the spectrum 
of the middle constituent of the triplets, as well as of the shift 
observed in the sextet from 6383'15, produced by a field of 
24,000 units. 

Shift in thousandths 


in thousandths 


of an A,U. 


of an A.U. 


+ 90 


+ 42 


+ 100 


+ 32 


+ 32 


+ 60 


+ 101 

The + sign meaning, as before, that the shift is in the direc- 
tion of greater wave lengths. 

Efforts were also made to measure the shifts of some of the 
lines which give more than three constituents. For example, 
Lohmann states that the line 6096 is divided into nine con- 
stituents. On my plates, there are three diffuse constituents, 
and there are doubtful signs of further subdivisions; but the 
latter are not sufficiently well marked, so that the measurements 
were made from the centre of the middle diffuse constituent. 
The same remark applies to 6678 and 6506 which are stated by 
Lohmann to divide into nine constituents, and to 6402 which 
is stated to divide into 15 constituents. There is no doubt that 
there is a shift of these lines towards the red end of the spectrum 
when tihey are vibrating in the magnetic field, but for the reason 
just stated, the measurements are not of the same degree of 
certainty as those obtained from the above triplets. 



Shift in thousandths of an A.U. 
+ 90 
+ 80 
+ 45 
+ 74 

The numbers indicate that the shift is different for different 

VOL. XV. PT. I. 


Mr Purvis, The radiation of various spectral 

lines ; and these differences eliminate any sources of error caused 
by a movement of the instrument. If there had been any such 
movement, it is obvious that the shifts would have been equal. 

There was a considerable increase in the luminosity of the neon 
when it was vibrating in the magnetic field ; and although the 
times of exposure and the other conditions were the same, the 
intensities of the unaltered lines when the gas was vibrating 
normally were weaker than the strongest constituents when they 
were divided. And in no case was the sharpness of the constituents 
equal to that of the unaffected lines, so that there was always 
some difficulty in measuring any shifts or separations. 

With regard to the intensities of the normal undivided neon 
lines it may be mentioned that my observations do not coincide 
exactly with those of Baly* or Lohmann, as the following table 
shows. But not much importance can be attached to observa- 
tions of this kind, unless the differences are clearly marked ; and 
possible variations in the efficiency of the dyed emulsion in various 
parts of the photographic plates should not be left out of con- 
sideration, although there are some differences which may indicate 
the influence of varying conditions of pressure and discharge in 
the tubes, as for example, in 5852 and 6717. 


























































































-The spectra of Neon, Krypton and Xenon," Phil. Trans. A. 202, 1904, p. 183. 

lines of neon, helium and sodium in a magnetic field. 51 

Also, in agreement with Lohmann's observations, and opposed 
to Baly's, no neon line at 6328"38 was observed on any of the 
plates; but, as in Lohmann's neon, there was a well marked one 
at 6835. 

Sodium. When the discharge through the neon was going 
on, the influence of the magnetic iield was to force it against 
the side of the glass capillary, so that small particles of the glass 
were illuminated, and the A and D,^ lines of the sodium in the 
glass were seen quite clearly. The divided constituents of these 
two lines were sharp and well defined, and they could be seen more 
easily than when a sodium flame was placed between the magnet 
poles. Lohmann used the same method in examining these lines, 
and the following table contains the results of the values obtained 
from my measurements compared with his, and also with those of 
Runge and Paschen, who used a Rowland grating and a field 
strength of 31,000 units*. 

Z>i. 5896-2 

A. 5890-2 



X 1013. 

- 5,89 s 

+ 2,92p 
+ 5,89 s 

-7,35 s 

- 4,43 s 

- 1,46^ 

+ 1,46^ 
+ 4,43 s 
+ 7,35 s 

Runge & Paschen 
- /\xlO". 


+ 3,02 
+ 5,95 


+ 1,48 
+ 4,32 
+ 7,39 


X^ X 24,000 

X 1013. 


+ 3,16 
+ 6,30 


+ 1,44 
+ 4,75 
+ 7,42 

The agreement between these numbers is only moderately 
good. It is difficult to explain the variations, for the ratio of 
2 : 1 of the constituents of A is fairly well maintained. The 
values are the close mean of 12 separate measurements on three 
separate plates ; and no changes in the strength of the field were 
observed during any of the experiments. 

Helium. One of the neon tubes contained some helium, for 
the triplet from the line 5875-618 was well marked in the photo- 

* Sitz. der Berl. Akad. 1902, p. 722. 


52 Mr Purvis, The radiation of various spectral lines, etc. 

graphic plates, and the following table contains the numbers 
obtained from the measurements of the separated constituents, 
compared with those obtained by Rayleigh quoted by Lohmann 
and by Lohmann himself. 



X 1013 



X 10i». 

' X2 X 24,000 

X 10". 



f - 4,09 s 
i p 

I + 4,09 s 


+ 4,33 


+ 4,58 

Lohmann's were eye observations, and they might not be so 
accurate as photographic ones. 

Furthermore, it may be that small variations in the amount 
and nature of the constituents of the glass of the tubes produce 
changes in the field between the magnetic poles ; and it is conceiv- 
able that some of the energy would be absorbed by these con- 
stituents, so that the full strength of the magnetic field would not 
act upon the gaseous particles of the vibrating gas. This view 
may explain the differences which have been noted in the 
numbers obtained when the Zeeman phenomena have been ob- 
served in gases. 

General Results. 

The results of these observations are : — 

(1) A comparison of the measurements of the constituents 
of various divided lines of neon, helium and sodium observed with 
an echelon grating by Lohmann and with a Rowland grating by 
the author. 

(2) The important difficulty in distinguishing the real con- 
stituents of a divided line from those of the adjacent images of 
other orders when an echelon grating is used for the observations, 
particularly when the line is divided into more than three con- 

(3) The measurements of the shifts of the divided consti- 
tuents of various neon lines towards the red end of the spectrum, 
and that the shifts are different for different lines. 

(4) A comparison of the intensities of the normal undivided 
lines of neon with those of Baly and Lohmann. 

I have to thank Professors Liveing and Sir James Dewar who 
were good enough to lend me two tubes of neon used in these 

Professor Nuttall, Trypanosoma lewisi, etc. 53 

The transmission of Trypanosoma lewisi hy fleas and lice. 
By G. H. F. NuTTALL, Sc.D., Quick Professor of Biology. 

[Read 23 November 1908.] 

The author described experiments, conducted in the Quick 
Laboratory, which demonstrated that Ceratophyllus fasciatus and 
Haematopinus spinulosus are capable of transmitting Trypanosoma 
lewisi. In one experiment, 3 fleas, transferred from a diseased to 
a healthy rat, gave a positive result. On the other hand, 30 — 60 
lice were required for the transmission of the trypanosome. No 
signs of any development of the trypanosomes were observed in 
the bodies of the lice. 

The presence of anticoagulin in the salivary glands of Argas 
persicus. By G. H. F. Nuttall, Sc.D., Quick Professor of 

[Bead 23 November 1908.] 

Experiments conducted with Mr C. Strickland have shown 
that the salivary glands and intestine of Argas persicus contain 
an anticoagulin which is inactivated by exposure to a temperature 
of 80° C. for 10 minutes. The organs of the tick do not contain 

54 Mj^ Dixon and Mr Hamill. Mr Dixon and Mr Harvey. 

The mode of action of specific substances. By W. E. DixoN, 
M.A., and P. Hamill, B.A. 

[Read 23 November 1908.] 

The action of secretin was first analysed, and it was shown 
that this substance produces its effect by chemical combination 
with the proferments in the pancreas. It was suggested that such 
substances of the hormone type have no direct action on living 
protoplasm. Other evidence was brought to show that drugs 
having a specific action on a definite tissue do not bring about 
that effect by chemical combination with protoplasm or with 
a constituent of the living cell. It was concluded that the mode 
of action of Galenical drugs was different from that of the 

The action of specific substances in toxaemia. By W. E. Dixon, 
M.A., and W. H. Harvey, B.A. 

[Bead 23 November 1908.] 

It was shown that certain toxins such as that of diphtheria 
cause death by vaso-motor failure. It was found that in animals 
affected with such a toxaemia death can be greatly delayed by 
the injection of normal saline solution. The action of drugs 
becomes progressively less according to the degree of toxaemia ; 
those drugs which act on the central nervous system are the first 
to lose their effect and those which act on muscle-fibre retain 
their characteristic effect longest. 

Mr Ghittock, The Migration Constants, etc. 55 

The Migration Constants of Dilute Solutions of Hydrochloric 
Acid. By C. Chittock, M.A., Trinity College. 

[Read 23 November 1908.] 

The experiments described in the present paper were under- 
taken with the object of throwing light on the cause of the 
abnormally low electrical conductivity of dilute aqueous solutions 
of strong acids and alkalies. It has long been known that whereas 
the equivalent conductivity of a neutral salt becomes approxi- 
mately constant at great dilution, that of a strong acid or alkali 
attains a maximum value at a dilution of about one-thousandth 
normal, and then decreases rapidly as the concentration is still 
further diminished. This decrease might be due to one of two 
causes ; first, to some interaction between the ions of the acid 
or alkali and the solvent, which might lead to a decrease in 
the amount of ionization or in the velocity of one or both of the 
ions ; or secondly, to some interaction with the small quantities 
of impurity which are always present in the most carefully pre- 
pared water. 

It was thought that measurements of the migration constant 
of an acid at varying degrees of dilution might be of assistance 
in deciding between these alternatives. If a small current is 
passed for a given time through a solution of some acid such as 
hydrochloric acid, hydrogen will be evolved at the cathode and 
oxygen at the anode. The total quantity of acid present will 
remain unaltered, but near the cathode there will be a loss of 
acid, and near the anode an equal gain. If it is assumed that 
the whole of the conductivity of the solution is due to the ions 
of the acid, measurements of these changes of concentration give 
us the means of calculating the ratio of the ionic velocities of 
hydrogen and chlorine. Such experiments would therefore enable 
us to determine whether the abnormally small conductivity of 
a dilute solution is associated with an abnormally small mobility 
of one of its constituent ions. 

Let u, V represent the velocities of the chlorine and hydrogen 
ions respectively under unit potential gradient. Then the migra- 
tion constant for the anion is given by ^ = u/(u + v). If a quantity 
of electricity Q coulombs is passed through the solution, the 
number of gram-equivalents of acid gained at the anode and 

lost at the cathode will be equal to -^-^ , where q (= 96440 

coulombs) is the charge carried by one gram-equivalent of 
either ion. 

56 Mr Chittock, The Migration Constants of 

Now let a definite volume V c.c. of the solution round the 
cathode be separated from the rest and stirred, this volume being 
large enough to contain the whole region in which any change 
of concentration has taken place. The concentration of this 
portion will then be less than its original value by an amount 

S?i = 1000^, 
q V 

hn being measured in gram-equivalents per litre. By measuring 
the change of concentration we can therefore find the value of p, 
and hence that of ujv. A second determination of the same 
quantity can be obtained in a similar way from the change of 
concentration at the anode. 

In determining the migration constants of very dilute solu- 
tions, it would be quite impossible to measure the changes of 
concentration by the ordinary methods of chemical analysis. The 
measurement of the electrical conductivity of such a solution 
affords however a sufficiently delicate method of obtaining its 
concentration, and this method has been employed in the pre- 
sent work. 

The experiments here described show that the apparent value 
of the migration constant of a solution of hydrochloric acid increases 
considerably as the concentration is diminished. It was thought 
that this result indicated a decrease in the velocity of the hydrogen 
ion as the cause of the low conductivity of the solution. A re- 
cently published paper by Whetham and Paine* shows however that 
another explanation is more probable. These authors have carried 
out a series of measurements on solutions of sulphuric acid, by 
a method similar in principle to that which has been employed 
by the present writer, and have found a change in the migration 
constant, which is similar, though smaller in amount, to that 
which has been obtained in the case of hydrochloric acid. They 
find that the change can be explained on the supposition that the 
conductivity of the solvent water is partly due to the presence 
of a salt formed from a weak acid and a weak base, such as 
ammonium carbonate ; this substance may be present in sufiicient 
quantity, owing to the absorption of atmospheric ammonia and 
carbon dioxide. A small quantity of ammonium carbonate would 
account for the observed change in the migration constant, and 
also for the decrease in the apparent equivalent conductivity of 
a dilute solution of acid or alkali. They therefore conclude 
that their experiments give no evidence in favour of the hypo- 
thesis that the velocity of the hydrogen ion becomes smaller at 
great dilution. 

The writer's experiments on hydrochloric acid had not been 
* Proc. Boy. Soc. lxxxi. A, p. 58. 

Dilute Solutions of Hydrochloric Acid. 57 

completed when the work of the above authors became known 
to him. The results already obtained had shown a large increase 
in the apparent value of the migration constant ; the degree of 
accuracy attained with the most dilute solutions was however not 
very satisfactory. The experiments have not been continued, 
since it appeared that no information as to the existence of any 
variation of the true mobility of the hydrogen ion would be 
obtained ; a short account of the method and of the preliminary 
results is however given. 


In conducting migration experiments with hydrochloric acid, 
it was considered advisable to keep the electrolysing current 
quite small, in order to prevent any evolution of chlorine at the 
anode ; the values deduced from the anodic and cathodic changes of 
concentration should then be equally trustworthy. For this reason 
the vessel used to contain the solution was arranged in such a way 
that a comparatively small volume of liquid near each electrode 
might be separated from the rest ; the resulting change in con- 
ductivity would thus be greater than if the liquid after the 
passage of the current were merely divided into two equal 

The cell is shown in Fig. 1. The main portion consists of 
a glass tube 1"3 cm. in diameter, bent into the form shown, the 
total length of the column of liquid from A^ to A^ being about 
80 cm. The current enters and leaves the solution by the 
electrodes J.i, J.2, which are of stout platinum foil, platinized 
and subsequently heated to redness. B^C^, BJJ^ are two pairs of 
electrodes which are used for measuring the resistance of the 
solution, connexion being made through the narrow tubes D, 
which are slipped over the platinum wires which support the 
electrodes, and fixed by sealing-wax. 

The upper end of each main tube is closed by the indiarubber 
bellows F, which forms an air-tight joint, and at the same time 
allows the electrode A to be raised and lowered for the purpose 
of stirring the liquid. The separation of the anodic and cathodic 
portions of the solution is carried out by increasing the pressure 
of the air at K ; the effect of this is to depress the liquid below 
the level of the bends at 8, S, and at the same time to cause it 
to rise at each end of the tube to some distance above the 
electrodes B, G. 

The solution is made up in the stoppered pipette M. A quantity 
of distilled water is placed in it, and the required amount of a 
standard solution of acid is then run in from a small filling vessel, 
which is weighed before and after the operation. The pipette with 

58 Mr Chittock, The Migration Constants of 

Fis. 1. 

Dilute Solutions of Hydrochloric Acid. 59 

its contents is now weighed, and the concentration of the solution 
can thus be calculated when that of the stock solution is known. 
Three such stock solutions were prepared ; the strongest ('2154 
normal) was estimated by precipitation as silver chloride, and the 
other two were obtained by diluting this with weighed quantities 
of water. The water used had an average conductivity of about 
10~^ reciprocal ohms at 18° C. 

The cell was immersed in a tank of water, which was well 
stirred and maintained at a temperature of 18° C. by means of 
a toluene regulator. 

The method of carrying out an experiment was as follows. 
The solution was made up in the pipette M, of which the delivery- 
tube was ground to fit the upper end of the vertical tube P. 
A current of air, purified from ammonia and carbon dioxide, was 
then slowly drawn through the cell, being introduced through the 
tube K and led out at G and H. The liquid was then run in 
from the pipette up to a mark on the tube at P, the volume of 
solution used being thus the same in all the experiments. The 
pressure over K was now increased, so that the liquid covered the 
electrodes B, G, and the resistance at each end measured several 
times by means of a commutator and galvanometer. 

The liquid was now brought back to its original position, and 
a current passed through the solution from Aj to A^, usually for 
about an hour. The current was obtained from a battery of about 
40 storage cells, and was measured by balancing the e.m.f. across 
the ends of a resistance included in the circuit (varying from 
2000 to 30000 ohms according to the strength of the solution) 
against the e.m.f. of a Clark cell. The current was maintained 
at a constant value by adjusting the applied e.m.f. by means of 
a potential-divider. 

After switching off the current, the pressure at K was again 
increased, and the separated portions of the solution stirred by 
means of the electrodes A. The resistance was then measured at 
each end, as at the beginning of the experiment. 

Let R, R be the measured resistances at the cathode before 
and after the passage of the current, k, k' the corresponding con- 
ductivities of the acid, and v) the conductivity of the water. We 
then have 

k' + w _R 

1 ^T n Bk 8R 

and therefore , = -^=^ , 

k + w R 

where SR = R' - R, 8k = k - k'. 

60 Mr Chittock, The Migration Constants of 

Hence, from the equation on p. 56, we obtain 


qV dn BR ,, . 

From the numbers given by Kohlrausch, a curve was plotted, 
with n as abscissa and k as ordinate. This curve is a straight 
line over the range covered by these experiments, and we may take 

the value of -^ to be constant. The value of k corresponding to 

the known concentration of the solution was read off from the 
curve, and the migration constant p calculated from the above 

The volume V of the separated liquid was determined as 
follows. The cell was placed in position in the tank, and filled 
with water up to the mark on the tube at P. It was then 
weighed. The separation was now carried out in the usual 
manner, the electrode on one side removed and dried, and the 
separated water extracted, the last drops being removed with 
filter-paper. The cell was again weighed, and the difference of 
weight gave the weight of water separated. The whole process 
was then repeated for the other side of the apparatus. 

The results of the experiments are given in the following 
table. The concentration n of the solution is given in gram- 



and time 





1-405 X 10-^ 


5-72 X 10-^ 
60 min. 




6-07 X 10-4 


2-86 X 10-4 
50 min. 




5-82 X 10-4 


2^87 X 10-4 
50 min. 




1-633 X 10-4 


60 min. 




1-035 X 10-4 


4-77 X 10-5 
60 min. 




1-006 X 10-4 


4-77 X 10-5 
60 min. 




Dilute Solutions of Hydrochloric Acid. 


equivalents per thousand grams of solution, and the current in 
amperes. The migration constant for stronger solutions of hydro- 
chloric acid, as measured by chemical methods, is given by Jahn* 
as "167, remaining the same for dilutions varying from 31 to 151 
litres per gram -equivalent. The strongest solution used in the 
present experiments was 712 litres per gram-equivalent. 

From this table a few experiments have been omitted, in which 
for some accidental reason the measurements on one side of the 
apparatus were not trustworthy. The check given by the agree- 
ment between the results obtained from the cathode and anode 
was considered of great importance, for in such dilute solutions 
absorption of impurities from the glass or from the air was very 
likely to occur during the progress of an experiment. In fact 
with the most dilute solutions there was generally a gradual 
increase of the measured resistance with time, which became 


Fig. 2. 

more marked when the liquid was stirred. This increase of re- 
sistance would however tend to increase the value of p deduced 
from the measurements at the cathode, and to diminish the value 
deduced from the measurements at the anode. No experiment has 
therefore been retained in which both results were not available. 

The values of the migration constant have been plotted against 
the cube root of the concentration in the diagram (Fig. 2). Jahn's 
value for the concentration n = ji^ is also given ; it is marked on 
the diagram by a circle. 

Discussion of Results. 

The change in the migration constant is much greater than 
that which has been observed by Whetham and Paine in the case 
of sulphuric acid. It has already been remarked that the numbers 

* Jahn, Zeitschr. f. Phys. Chem. vol. lviii. p. 641 (1907). 

62 Mr Ghittock, The Migration Constants of 

obtained with the most dilute solutions are not very trustworthy, 
mainly owing to the fact that the measured resistances did not 
remain constant, but generally increased with time. We can 
easily see however that the change is too great to be explained 
by a decrease in the mobility of the hydrogen ion. It has already 
been mentioned that the curve obtained by plotting the con- 
ductivity A; of a solution of hydrochloric acid against the concen- 
tration n is a straight line which does not pass through the 
origin ; it can however be made to do so by increasing the values 
of A; by a constant quantity, equal to 3"7 x 10~®. This " corrected" 
curve we may then take to represent the relation between k and n 
which would hold if the acid were completely ionized, and the 
hydrogen ion possessed its maximum mobility. From the difference 
between the ordinates of the actual and the " corrected " curve 
for any given value of n, we can find what reduction in the 
velocity of the hydrogen ion would produce the observed dimi- 
nution of conductivity. Making the calculation for a concentration 

6 X 10~* (n^ = '084), we find that the decrease in velocity would 
be such as to cause an increase in the migration constant from 
•167 (the normal value) to -170. The value given by the curve 
(Fig. 2) for this concentration is "lOl. The theory of diminished 
mobility of the hydrogen ion is thus seen to be insufficient to 
account for the observed change. 

Let us now consider the alternative hypothesis, that the in- 
crease in the migration constant is an apparent one merely, and 
is due to the presence, in addition to the acid, of some neutral 
substance of which the velocities of the anion and cation are 
more nearly equal to one another than are those of hydrogen and 
chlorine. Whetham and Paine have calculated the effect of such 
an impurity, and have shown that if the difference of mobility 
of its anion and cation is small compared with the mobility of 
the hydrogen ion, the migration constant is increased in the ratio 
{ku -f k'v)/{k + k') u, where k, k' are the partial conductivities of 
the hydrochloric acid and of the second substance respectively, 
u the mobility of the chlorine ion, and v that of the hydrogen 
ion. If then we calculate from this result the value of k' which 
would give the observed rise in the migration constant, we find 
k' = 8-7 X 10-«. 

The conductivity of the water used as solvent in the two 
experiments, in which the concentration was approximately 
6 X 10~* gram-equivalents, was 9"7 x 10~^ reciprocal ohms. It 
is clear therefore that this water did not contain a sufficient 
quantity of any neutral salt to produce the observed effect. It 
was preserved in vessels of Jena glass or of platinum ; the pipette 
in which the solutions were made up, and the migration cell 

Dilute Solutions of Hydrochloric Acid. 63 

itself, were however constructed of soft glass. It is however 
quite impossible that the conductivity of the water could have 
been greatly increased by solution of the glass ; in one case 
a solution of which the strength was 1"63 x 10~^ gram-equivalents 
per litre was allowed to stand in the pipette for a period of three 
days, and the conductivity at the end of that time did not differ 
by more than 2 per cent, from Kohlrausch's value. 

The observed results can probably be explained if we suppose 
that the principal impurity in the water was ammonia dissolved 
from the air. The ionization of ammonia is small, even in very dilute 
solution ; when hydrochloric acid is added, ammonium chloride, 
which is highly dissociated, is produced. The partial conductivity 
of the ammonium chloride will then be considerably greater than 
the conductivity of the original ammonia, and the quantity present 
may be sufficient to produce the observed change in the apparent 
migration constant for the solution. 

It is interesting to note, that Whetham and Paine concluded 
from their experiments that the impurities in their water prob- 
ably consisted of ammonium carbonate together with an excess 
of carbonic acid. Goodwin and Haskell*, in an investigation of 
the conductivity of dilute solutions of hydrochloric and nitric 
acids, found that different samples of water, although their con- 
ductivities might be equal, gave solutions of which the conduc- 
tivities were markedly different ; the conductivity of the acid, 
corrected for the effect of impurities, was however the same in 
all cases. The large difference between the results of the present 
experiments and those of Whetham and Paine is therefore prob- 
ably due to the specific effects of different impurities, and affords 
additional evidence in favour of the theory that both the change 
in the migration constant and the drop in the equivalent con- 
ductivity curve are due to an interaction between the acid and 
the impurities present in the solvent. 

The author desires, in conclusion, to express his thanks to 
Professor Sir J. J. Thomson for his kind interest and encourage- 
ment during the progress of the work. 

* Goodwin and Haskell, Physical Review, Dec. 1904. 

64 Prof. Thomson, On the Carriers of the Positive Charges, etc. 

On the Carriers of the Positive Charges of Electr-icity emitted 
by hot wires. By Sir J. J. THOMSON, M.A., F.R.S., Cavendish 
Professor of Experimental Physics. 

[Read 9 November 1908.] 

A series of measurements of the values of e]m for the posi- 
tively electrified particles given out by a strip of platinum wire 
heated to incandescence were made by the method described by 
the author in a paper on 'Positive Rays of Electricity,' Phil. Mag. 
Oct. 1908. When the platinum had been kept for several days in 
a high vacuum and heated repeatedly to incandescence, the value 
of ejm for the great majority of the positively charged particles 
was about 10727, showing that the mass of the particles was 
about 27 times the mass of an atom of hydrogen. The masses 
of molecules of CO and N^ are 28 times that of an atom of 
hydrogen, and these molecules could not be distinguished by 
determinations of ejm. The spectroscopic examination of the gas 
given off by the hot wire after prolonged heating showed that the 
CO spectrum was bright while that of nitrogen could not be 
detected. For this reason I think the carriers of the positive 
electricity are molecules of CO and not N2. 

After the platinum by long continued heating had been 
brought into a state when the carriers had for the most part the 
mass of a molecule of CO, hydrogen was let into the vessel and 
the platinum foil made red-hot in an atmosphere of hydrogen, the 
hydrogen was then pumped out ; determinations of e/m after this 
process had been gone through showed that the average mass of 
the carriers was only 8 or 9 times that of the hydrogen atom, 
thus the absorption of the light gas by the platinum had 
diminished the average weight of the carriers to about one-third 
of its original value ; this I think shows that the carriers of the 
positive electricity given out by hot metals are for the most part 
the molecules of gas absorbed by the metal. I have much 
pleasure in thanking Mr G. W. C. Kaye for the assistance he has 
given me in making these experiments. 

Vrof. Thomson, On the Electric Theory of Gravitation. 65 

On the Electric Theory of Gravitation. By Sir J. J. Thomson, 
M.A., F.R.S., Cavendish Professor of Experimental Physics. 

[Read 9 November 1908.] 

The view that gravitational attraction is due to a slight excess 
of the attraction between unlike charges of electricity over the 
repulsion between like charges is a very old one, indeed it seems 
to have been regarded by some writers as almost a part of the one 
fluid theory of electricity. The theory is an interesting one 
because it involves the existence of effects which do not seem to 
be hopelessly too small to be tested by experiment : some of these, 
relating to the possible influence of the velocity of the attract- 
ing bodies on the gravitational attraction between them, have 
recently been considered by Lorentz. At the end of this paper 
I shall indicate another result of the theory which is of so special 
a character, that if it were established by experiment, it would 
follow almost as a matter of course that gravity must be due to 
something very closely connected with electrical action. 

Before discussing this effect I will consider the theory from 
the point of view of stresses in a medium between the attracting 
bodies. In one form of electrical theory we suppose that the 
stress in the ether is altered by the passage through it of lines of 
electric force, in such a way that the tension along the lines of 
force and the pressure at right angles to them is increased by an 
amount proportional to the square of the density of the lines of 
force. "When we endeavour to use lines of electric force to describe 
the state of the magnetic field or of fields through which electrical 
waves are passing, I think there are considerable advantages in 
regarding the lines of electric force from a somewhat different 
point of view from that usually adopted in electrostatics. In 
that subject it is usual to take as the lines of force due to say a 
positive charge e at ^, and a negative charge — e at 5, as the 
lines whose directions are the resultants of the radial forces 
e/AP^ and —ejBP^, radiating from A and B respectively. We 
might however regard the lines of force as consisting of two sets, 
one set being straight lines radiating from A, the other straight 
lines radiating from B. We might, that is, regard the component 
fields of which the actual field is made up as having an actual 
physical existence, and suppose that it is the effect they produce 
and not their structure which is modified when several of them 
exist simultaneously in the same field. We can illustrate the 
difference between the two methods by considering the case of 
two parallel vertical planes A and B, A being on the left of B, 

VOL. XV. PT. I. 5 

66 Prof. Thomson, On the Electric Theory of Gravitation. 

the one having a positive the other an equal negative charge. On 
the usual view, lines of force only exist between A and B, the 
lines starting from the positive charge on A and ending on the 
negative charge at B ; the region to the left of A or the right of B 
being free from lines of electric force. On the other view positive 
lines of force start from A both to right and left, and also negative 
lines of force from B. In the region between A and B we have 
the positive lines in one direction and the negative in the opposite, 
both giving a contribution of the same sign to the electric force ; 
while on the left of A and the right of B the negative and the 
positive lines run side by side in the same direction and, as far 
as the electric force goes, neutralize each other's effect. 

The advantages of the second method are most felt when the 
electric charges are moving and there is a magnetic as well as an 
electrostatic field, the magnetic force at any point being regarded as 
due to the movement of the lines of electric force at that point, and 
proportional to the vector product of the number of lines of electric 
force and the velocity of these lines. Thus suppose the plate A 
is rotating while 5 is at rest, on the second view of the disposition 
of the lines of force in the field, all the positive lines of force 
rotate with A, thus there is motion of these lines, and therefore 
magnetic force throughout the whole of the field and not merely 
between the plates A and B: and we know from experiments that 
the magnetic force does exist throughout the whole region and is 
not localized between A and B. If we take the first view that 
the lines of force, due to the charges on A and B, are confined to 
the region between A and B, then the rotation of A would only 
set these lines in motion in the space between A and B, this 
motion would only account for the magnetic field between the 
plates, and we should have to introduce further hypotheses to 
account for the magnetic forces which as experiment shows exist 
in the other regions. 

If we consider the differences which exist between the 
properties of negative and positive electricity, the negative being 
located on corpuscles, the positive on bodies of atomic dimensions, 
it does not seem by any means impossible that there may be 
some difference between the positive and the negative lines of force^ 
at any rate the effects of such a difference seem a legitimate 
subject for discussion. 

Let us take the case where all the lines of force are parallel 
to the axis of x, and suppose that through unit area, at right 
angles to x, there are P positive lines of force running in the 
direction in which x increases, N negative lines of force in the 
same direction ; then on the usual theory of stress in the medium, 
in which we do not distinguish between the effects of positive 
and negative lines, these lines increase the tension along the 

Trof. Thomson, On the Electric Theory of Gravitation. 67 

lines of force by k(P — Ny where k is a constant. If we dis- 
criminate between the effect of positive and negative lines we 
must replace this expression by 


where a, yS, 7 are not necessarily equal to each other. On this 
assumption let us calculate what would be the attraction between 
two slabs of matter A and B. Suppose that for each unit of 
surface of A there are Pi units of positive electricity, N-^ of 
negative, while Pg and N2 are the corresponding qua,ntities for B. 


A B 



Fig. 1. 

If P is the number of positive lines of electric force through 
unit area, iV the number of negative, then we see that between 
the plates 

to the right of B, 

P = l{P, + P,\ N = ^{N, + N,), 
to the left of A, 

P = -^{P^ + P.), i\r=-i(i\r, + i\r^). 

The force on unit area of B towards A will be the tension in 
the region between A and B minus that in the region to the right 
of B, i.e. it will be equal to 

- {\a{P, + P,y + i^{]^, + N,y - i7 (P, + P,) (N, + iV^)} 

= -aP,P,-fiN,N, + y{P,N, + P,N,) (1). 

Let us take the case when both A and B are electrically 
neutral, i.e. when Pi = Ni, P2 = i\^2, then this force will be equal to 

{2y-{oi + ^)}P,P,. 

68 Prof. Thomson, On the Electric Theory of Gravitation. 

If we suppose that the atoms of the different elements are 
electrical systems, and that each atom contains a number of units 
of positive and also of negative electricity proportional to the 
atomic weight, then Pj and Pg will be proportional to in^, ma, the 
masses of unit areas of the slabs J. and P, so that the attraction 
between the slabs will be proportional to {27 — (a + /3)} miWs. 
Thus the attraction between two infinite slabs will be proportional 
to the product of their masses and independent of the distance 
between them, it follows from this that the attraction between 
finite masses separated by distances large compared with their 
linear dimensions, will vary inversely as the square of the distance 
between them. 

If we take the number of positive units of electricity in the 
atom as equal to the atomic weight, then using the electrostatic 
system of units 

P P 

=^ = =^ = 10^ X 3 X 10i«, 

when mi and mo are measured in grammes. 

Thus the attraction between the slabs 

= {27 - (a + y8)} 9 X 10^ mima. 

The gravitational attraction between the slabs is 

27r X 6*6 X 10~^ x miin^, 

hence if the attraction we are considering is the gravitational 

27 - (a + y8) = Q X 10^^ 

But a, /3, 7 are all very nearly equal to I/Stt, hence 

g y-<"+^> ^i-2xio-'. 


If in equation (1) we put N-^^^N^^ 0, we see that the repulsion 
between these charges is aP^P^, if we put P^ = P^ = 0, the repulsion 
is ^NiN^, and if we put iV^i = 0, P2 = 0, the attraction is yPilSf^, 
thus a is proportional to the force between two unit positive 
charges, /3 to the force between two unit negative charges and 7 to 
the attraction between a unit positive and a unit negative charge. 
It is to be noted that unless a = yS = 7, we have to amend the de- 
finition of unit charges usually given, as in this case, if the force 
between two units of positive charge at unit distance is the unit 
force, the force between two units of negative charge will not be 
so. If we recognise these differences between positive and nega- 
tive electricity the definition of an unelectrified body is a matter 

Prof. Thomson, On the Electric Theory of Gravitation. 69 

of some delicacy unless we have recourse to the atomic theory of 
electricity, and define an unelectrified body as one which contains 
equal numbers of positive and negative units of charge. 

The weight of a body on this view depends only on the charges 
of electricity it contains, thus if we suppose an atom of hydrogen 
to contain one positive and one negative charge, the weight of an 
atom of hydrogen would only be twice that of a corpuscle which 
contains one negative unit, but the mass of the hydrogen atom is 
1700 times that of the corpuscle, hence the acceleration of the 
corpuscle under gravity would be 850 times that of an atom of 
hydrogen, or 850 x 981 ; if the atom of hydrogen contained n 
units of positive and n of negative electricity the acceleration of 

the corpuscle would be - 850 x 981, hence on this view we should 
^ n 

expect the acceleration of the corpuscle under gravity to be very 

much greater than that of ordinary matter. At present the 

detection of an acceleration of the corpuscle as great even as 

850 X 981 would seem to be beyond the powers of known methods, 

but not so much beyond as to preclude the hope that with such 

improvement as we may reasonably expect in the manipulation 

of slow cathode rays it may ultimately be capable of investigation. 

70 Prof. Thomson, On the Distribution of Electric Force, etc. 

On the Distribution of Electric Force along the Striated Dis- 
charge. By Sir J. J. Thomson, M.A., F.R.S., Cavendish Professor 
of Experimental Physics. 

[Read 9 November 1908.] 

A Wehnelt hot lime cathode was used to produce the discharge 
as it was found that at low pressures the striations produced in 
this way were remarkably steady and bright and in consequence 
made accurate measurements of the distribution of electric force 
much easier than with the ordinary discharge. It was found that 
just in front of the bright surface of a striation towards the 
cathode there was a reversal of the electric force. This reversal 
causes a great accumulation of ions in the part of the striation 
nearest the cathode, the recombination of the ions in this region 
will therefore be much greater than elsewhere and it is shown 
that a very simple explanation of the formation and behaviour of 
striations was given by the hypothesis that the recombination of 
the ions was the source of the luminosity in the striations. 



The Laws of Mobility and Diffusion of the Ions formed in Gaseous Media. 

By E. M. "Wellisch. (Communicated by Sir J. J. Thomson) . 1 

TTie Radioactivity of Ruhidi^(,m. By Norman Campbell . . . 11 

On the Free Fressitre in Osmosis. By L. Vegard. (Communicated by 

Sir J. J. Thomson.) (Two figs, in Text) . . . . . .13 

Therapeutic Inocidation for Generalised Bacterial Infections. By L. 
Noon. (Commixnicated by Professor G. Sims Woodhbad.) (Six 
figs, in Text) ... . ... . . . .24 

On the examination of living leucocytes in vitro. By Constant Ponder. 

(Communicated by W. E. Dixon.) (Two figs, in Text) . . . 30 

On the Relation hetween Ionization and Pressure for Rontgen Rays in 
different Gases. By J. A. Crowther. (Communicated by Sir J. J. 
Thomson.) (Two figs, in Text) . . . . . . .34 

On the Relative Ionization produced by Rontgen Rays in different Gases. 

By J. A. Crowther. (Communicated by Sir J. J. Thomson) . 38 

The Relationship hetiveen Human and Bovine Tubercidosis. By Professor 

G. Sims "Woodhead . . . . . . . . • • 40 

The radiation of various spectral lines of neon, helium and sodium in a 

magnetic field. By J. E. Purvis . . . . . . . 45 

The transmission of Trypanosoma lewisi by fleas and lice. By Professor 

G. H. F. NUTTALL . . . . . . '. . . .53 

The presence of anticoagulin in the salivary glands of Argas persicus. 

By Professor G. H. F. Nuttall , 53 

The mode of actio7i of specific substances. By W. E. Dixon and 

P. Hamill . ... . . . . . . . 54 

The action of specific substances in toxaemia. By W. E. Dixon and 

W. H. Harvey . . .54 

The Migration Constcmts of Dilute Solutions of Hydrochloric Acid. By 

C. Chittock. (Two figs, in Text) . -. . . . . . 55 

On the Carriers of the Positive Charges of Electricity emitted by hot tvires. 

By Sir J. J. Thomson . • .64 

On the Electric Theory of Gravitation. By Sir J. J. Thomson. (One fig. 

in Text) . . . . . • . ■ ■ ■ ■ - 65 
On the Distribution of Electo'ic Force along the Striated Discharge. By 

Sir J. J. Thomson . . . 70 




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Camk&g^ ^]^Hai50p]^kaI Somtg. 

On a configuration of twenty-seven hyper-planes in four- 
dimensional space. By Professor W. Burnside, F.R.S. 

[Beceived 23 January 1909.] 
[Bead 9 February 1909.] 

Clifford has shewn the existence of a plane figure con- 
sisting of 2** circles and 2** points such that each circle passes 
through n + 1 of the points and each point lies on n-\-l of the 
circles*. If this figure be inverted with respect to a point outside 
its plane, the circles become plane sections of the sphere into 
which the original plane inverts. The configuration may then be 
specified as one of 2'* planes and 2** points, such that in each plane 
lie n + 1 of the points and through each point pass w + 1 of the 
planes. The set of points is, however, restricted to lie on a sphere, 
or, if the configuration is modified by a projective transformation, 
on a quadric. 

That such a configuration exists, apart from the restriction of 
the points to lie on a quadric, is true ; and I believe a proof of 
the fact has been published though I cannot give a reference 
to it. 

In Mr Grace's memoir a proof is given of the existence of some 
very remarkable configurations of spheres and points in three- 
dimensional space (pp. 182 — 188). If one of these, regarded as 
existing in four-dimensional space, be inverted with respect to 
a point, not in the three-dimensional space of the configuration, 

* Clifford, Collected Papers, pp. 51, 52. See also J. H. Grace, " On circles, 
spheres and linear complexes" (Camb. Phil. Trans. Vol. xvi. pp. 153-190), with 
which memoir this note is more directly connected. 

VOL. XV. PT. II. 6 

72 Prof. Burnside, On a configuration of twenty-seven 

there results a configuration of points and hyper-planes ; a certain 
number of hyper-planes passing through each point and a certain 
number of points lying in each hyper-plane ; with the restriction 
that the whole of the points lie on a four-dimensional quadric. As 
in the previous case this restriction is not a necessary condition 
for the existence of the configuration. The object of the present 
note is partly to prove this result in a particularly interesting case, 
and partly to bring out the tactical analogy (which the numbers 
suggest) of the configuration of 27 hyper-planes with the con- 
figuration of 27 lines on a cubic surface. 

To avoid the continual use of the word hyper-plane, a flat 
manifold in four-dimensional space, determined by four points, is 
called simply a plane ; and when it is necessary to refer to one 
determined by three points it is called a three-dimensional plane. 

A quadric in four-dimensional space is determined by fifteen 
points. Eleven points therefore determine four linearly inde- 
pendent quadrics. Every one of a system of quadrics through 
eleven points must therefore have five other common points. 
This and the fact that four points determine a plane and four 
planes determine a point forms the basis of the reasoning. 

1. In a four-dimensional space, consider a base-point 0, and 
five planes, 

1, 2, 3, 4, 5, 

passing through it. On the line of intersection of each set of 
three planes, mark a point distinct from ; and denote the 
point on the line of intersection of 1, 2 and 3 by 123. (In this 
symbol the sequence of the figures is immaterial.) Denote the 
plane which passes through 123, 124, 134, and 234 by 1234. 
(In this symbol again the sequence of the figures is immaterial.) 
Then the five pairs of planes 

1,2345; 2,1345; 3,1245; 4,1235; 5,1234, 

are a set of quadrics through 11 points, viz. and the 10 points 
123, etc. Hence they determine a set of 5 further points, which 
lie on all the quadrics, so that 8 of the 16 lie in each plane. Of 
these 5 then, one must lie on 1 and the other four on 2345. That 
one of the five which lies on 1 cannot also lie on 2 ; and a suitable 
notation for the five points in what follows will be 

16, 26, 36, 46, 56, 

(here the sequence of the figures is essential), where 16 lies in the 
five planes 

1, 1345, 1245, 1235, 1234. 

The figure thus constructed is a complete one in the sense that 
each point (and each plane) bears the same relation to the figure 

hyper-planes in four -dimensional space. 73 

as any other point (or any other plane). Through each point five 
planes pass, as given by the table 

1, 2, 8, 4, 5; 

123 1, 2, 3, 1234, 1235; 

16 1, 1345, 1245, 1235; 1234; 

and the points and planes admit simultaneous groups of permuta- 
tions for which the tactical relations of this table are unaltered. 
The order of this group is 2* . 5 ! ; and as it affects the planes it is 
generated by 

(1, 2345) (2, 1345); 
(1, 2) (2345, 1345); 
(1, 2, 3, 4, 5) (2345, 1345, 1245, 1235, 1234). 
It contains an Abelian group of order 16, as a self-conjugate sub- 
group, and in respect of this is isomorphic with the symmetric 
group of degree 5. 

2. Take now six planes, 

1, 2, 3, 4, 5, 6, 
all passing through the base point ; and on the 20 lines of inter- 
section of each set of three mark arbitrary points 123, etc. With 
each set of five planes, out of the six, carry out the above construc- 
tion, so that there arise fifteen fresh planes 1234, etc.; and thirty 
fresh points 16, etc. For convenience of reference the set of 
(1 -I- 20 -I- 30 = 51) points thus arrived at may be denoted by 8q. 
The figure so far is obviously not complete in the sense already 
explained. That part of the figure which lies in the plane 
(three-dimensional space) 1, consists of 16 points, 0, 123, ... , 156, 
12, ... , 16 and 15 three-dimensional planes, viz. the intersections 
of 2, ... , 6, 1234, ... , 1456 with 1. This is one of the figures 
referred to in the introduction and is completed by noticing that 

12, 13, 14, 15, 16 
lie in a three-dimensional plane. 

Take now 123 as a base point. Through it pass just six of the 
planes connected with 0, viz.: 

1, 2, 3, 1234, 1235, 1236. 
On each of 19 out of the 20 lines of intersection of these planes 
one point (besides 123) of the set S^ lie. Thus 

on 1, 2, 3 there lies 0, 

1, 2, 1234 „ 124, 

1, 1234, 1235 „ 16. 

On the line of intersection of the three planes 1234, 1235, 

1236 there is no point of the set S^. On this line mark an 

arbitrary point 1'2'3', distinct from 0. With 123 as base point, 

the six planes through it and the twenty points (including 1'2'3') 

on their lines of intersection, complete the construction of the 


74 Prof. Burnside, On a configuration of twenty -seven 

beginning of this paragraph. Of the thirty additional points that 
arise it will be found that twenty-one belong to the set Sq, viz.: 

145, 245, 345, 45, 54, 12, 21, 

146, 246, 346, 46, 64, 13, 31, 
156, 256, 356, 56, 65, 23, 32. 

The remaining nine, adhering to the notation already used, 
may be represented by 

1'2'4', 1'2'5', 1'2'6', 

1'3'4', 1'3'5', 1'3'6', 

2'3'4', 2'3'5', 2'3'6' 

(the sequence of the figures is immaterial), 1'2'4' being the point 

common to the five planes 

1234 1245 1246 
(24, 25, 26, 1'2'3') and '(14, 15, 16, 1'2'3'). 

Since 12, 13, 14, 15, 16 lie in a three-dimensional plane, the 
two latter planes may be written 

(21, 23, 24, 25, 26, 1'2'30, (12, 13, 14, 15, 16, 1'2'3'). 

Instead of 123 any of the twenty points of which it is one 
might be taken to make the last construction, and whichever is 
chosen one point must be arbitrarily chosen on a certain line 
before the construction can be carried out. The construction 
however, having led to a point 1'2'4' on the line of intersection of 
1234, 1245, 1246, it is now possible to take 124 as a base point 
and, without introducing any further arbitrary element, to carry 
out the construction from this point. When this is done it is 
found that of the thirty additional points that arise twenty-one 
again belong to the set S^, and the remaining nine are 

1^2^3^ V^'b', V2'Q\ 

1%'^', 1%%', 1%'Q', 

2'4'3', 2'4'5', 2'4'6' 

where 1'2'3' is the point common to the five planes 
1234, 1235, 1236, 
(12, 13, 14, 15, 16, 1'2'40 and (21, 23, 24, 25, 26, 1'2'4'). 

Comparing this with the specification of 1'2'4', it follows that 
1'2'3' is the same point as 1'2'3'. 

Similarly 1^2^5^ V2'&, 1%'^' and 2^4^3^ are found to be 

identical with 1'2'5', 1'2'6', 1'4'3' and 2'4'3'. Hence, the point 
1'2'3' having been once chosen, w^hen the construction of the 
beginning of this paragraph is carried out with each of the twenty 
points 123, ... , 456 in turn, besides the set S^ a set of just twenty 
points (including 1'2'3') and no more will arise 

hyper-planes in four- dimensional space. 75 

Moreover, since 

(12, 13, 14, 15, 16, 1'2'3', 1'2'40 
is a plane, it follows immediately that the fifteen points 
12, 13, 14, 15, 16, 1'2'3', 1'2'4', 1'2'5', 1'2'6', 

1'3'4', 1'3'5', 1'3'6', 1'4'5', 1'4'6', 1'5'6' 
all lie in a plane. Call this plane 1' and the other five that arise 
in the same way 2', 3', 4', 5', 6'. 
Through 16 pass the five planes 

V, 1345, 1245, 1235, 1234. 

On the lines of intersection of V , 1245, 1235, 1234, there 
lie the points 26, 1'2'5', 1'2'4', 1'2'3', and the plane through 
these points is the plane 2'. Hence from the configuration of 
§ 1, the planes 1', 2', 3', 4', 5' meet in a point through which 
6' must clearly pass. Call this point 0'. There is then finally a 
set of 27 planes, viz. : 

1, 2, 3, 4, 5, 6, 

1234, 1235, , 8456, 

1', 2', 3', 4', 5', 6'; 
and 72 points, viz. : 


123, 124, , 456, 

12, 21, , 56, 65, 

1'2'3', r2'4', , 4'5'6', 


Through each point pass six planes and in each plane lie 
sixteen points, and the configuration is complete. The relations 
are given by the scheme 

1, 2, 3, 4, 5, 6; 

0' r, 2', 3', 4', 5', 6'; 

123 1, 2, 3, 1234, 1235, 1236; 

4'5T 4', 5', 6', 1456, 2456, 3456; 

12 1, V, 1456, 1356, 1346, 1345; 

21 2, 2', 2456, 2356, 2346, 2345. 

A very slight modification in the notation, viz. the replacing of 
the symbol 1234 by (56) (the brackets will prevent confusion 
between the symbol for a plane and the symbol for a point) gives 
these relations a well-known form. In fact with Schlafli's nota- 
tion for the 27 lines on a cubic surface, the table gives the 
36 double-sixers that can be constituted from them. The tactical 
analogy between the 27 hyper-planes and the 27 lines on the 
surface is thus obvious ; and the hyper-planes and points admit a 
group of 51,940 permutations for which the relations given by the 
table are invariant. 

76 Mr Wilhs, Note on some double fluorides of sodium. 

Note on some double fluorides of sodium. By W. A. R. Wilks, 
B.A., Caius College. (Communicated by Dr Fenton, F.R.S.) 

[Read 8 February 1909.] 

Many of the insoluble compounds by which elements are 
quantitatively estimated are, as might be expected, found in 
nature as minerals. Hence it was thought probable that if sodium 
could be estimated by means of some simple inorganic compound 
the latter would be found as a mineral. On considering the 
simple minerals containing sodium, the only one which might be 
suitable for the purpose appeared to be cryolite. 

This compound has been artificially prepared by Deville {An. 
Ch. Ph. (8) 59, 82, 1860) and by Baud. The former saturated 
hydrofluoric acid by sodium carbonate and alumina in the propor- 
tion of three molecules of carbonate to one of alumina, evaporated 
and obtained the substance 3NaF . AIF3. The latter precipitated 
a solution of aluminium fluoride by sodium fluoride and obtained 
the hydrate of cryolite 6NaF.2AlF3.7HoO. This hydrate is 
gelatinous and is soluble in water to the extent of '352 gms. per 
100 c.c. at 16° C. Natural cryolite which is SNaF.AlF^ has the 
solubility "034 gms. in 100 c.c.'s at 15°. 

In order to find whether sodium could be detected as double 
fluoride, aluminium was dissolved in dilute hydrofluoric acid in a 
platinum dish until the acid was exhausted. On adding this 
solution to a solution of sodium chloride a gelatinous precipitate 
was obtained whose composition has not yet been determined. If 
the sodium chloride was dilute, however, the precipitate did not 
appear. It was further observed that boiling the solution facili- 
tated the precipitation and that in this case the precipitate was 
no longer gelatinous but crystalline. It was also found that 
acids had a marked solvent action on the precipitate. After 
these preliminary observations another mode of preparation of 
the precipitant was resorted to. 

Precipitated aluminium hydroxide which has been simply 
dried by a filter pump was added to a small quantity of strong 
hydrofluoric acid in a platinum dish. The hydroxide seems to 
exhaust the acid much better than does aluminium itself, and in 
the process of solution the moist hydroxide furnishes sufiicient 
water to form a solution of convenient strength. In order to get 
the best results the hydrofluoric acid is allowed to stand for at 
least two days in contact with excess of hydroxide. The complex 

Mr Wilks, Note on some double fluorides of sodium. 77 

hydrofluoaluminic acid formed is then so stable that hydrofluoric 
acid does not seem to be split off even on boiling. The solution 
was in fact boiled in a test tube for half an hour without any 
apparent action on the glass. 

To diminish the concentration of hydrogen ions in the resulting 
solution, an acetate must be added. The acetates of nickel or 
copper can be used for this purpose as neither of these metals give 
precipitates of double fluorides. Hence to the hydrofluoaluminic 
acid solution an equal bulk of a cold saturated solution of copper 
acetate is added. This solution is then boiled and any slight 
precipitate filtered off. To this solution an equal volume of a 
50 per cent, solution of alcohol is added. This makes the reaction 
still more sensitive. Care must be taken however not to add too 
much alcohol, otherwise a precipitate will be formed which appears 
to be redissolved only with difficulty on adding more water. If 
this precipitant has been carefully made the test for sodium can 
be carried out in test tubes. 

The test is carried out as follows. About 5 c.c. of the precipi- 
tant is boiled in a test tube and then the sodium solution added. 
If the latter is strong there will be an immediate precipitate. If 
it is very weak, however, it will be required to be boiled for some 
time before the precipitate appears. To make quite certain that 
the precipitation was not due to action on the glass a blank 
experiment was carried out at the same time in another tube 
without adding sodium chloride. In this case there was no pre- 
cipitate. The test appears to be very delicate, one part of sodium 
chloride in 20,000 parts of solution being readily detected. 

The precipitate in these cases has not the composition of 
cryolite. Analysed by heating with strong sulphuric acid and 
weighing the sodium sulphate and alumina it seems that sodium 
and aluminium are present in the atomic proportions of 1 . 1 : 1. 
Further analyses are however being carried out. 

Pure potassium and ammonium salts are not precipitated 
under the conditions stated above. The metals other than sodium 
which give precipitates are silver, magnesium, calcium, strontium, 
barium and lead. 

Attempts are now being made to determine whether sodium 
can be quantitatively estimated in this way. It has already been 
proved that precipitation is almost if not quite complete. 

It was considered possible that the elements related to 
aluminium treated in the same way would give precipitates with 
sodium. It was found that ferric hydroxide dissolved in hydro- 
fluoric acid gave with sodium a light brown precipitate which has 
not yet been examined. 

Chromium and beryllium, however, fail to give a precipitate 
even with concentrated solutions of sodium chloride. 

78 Mr Vegard, An experiment on ionisation with 7 o^ays. 

An experiment on ionisation with 7 rays. By L. Vegard, 
Cand. real, Universitetsstipendiat of tlie University of Christiania. 
(Communicated by Professor Sir J. J. Thomson.) 

[Bead 8 March 1909.] 

1. When a gas is ionised by Rontgeu or 7 rays, we are led to 
consider the action of ether waves or pulses upon the molecules of 
a gas. In order to explain the small amount of ionisation it is 
necessary to assume that the various molecules are in a different 
position relative to the pulse. Several possibilities are discussed 
by Sir J. J. Thomson in his book. Conduction of Electricity through 
Gases. As a way in which the molecules can have a different 
position relative to the pulse, he mentions the possibility that the 
wave-front has a structure. There is, however, another manner 
in which a different relative position could arise even when we 
assume a continuous wave-front, namely if the molecule had 
certain directions of ionisation. 

The directions of the electric forces in a set of pulses travelling 
in the same direction must lie within narrow limits, e.g., all nearly 
parallel or perpendicular to a certain line. Now for a molecule to 
become ionised it might be required that the electric force should 
act in a certain direction relatively to some axis in the molecule, or 
it might require a series of pulses along this same direction. 

If such conditions were necessary for ionisation, it would 
naturally cut down to a great extent the number of molecules 
ionised by the rays. It might possibly not be the only condition, 
but if in general n conditions, 1, 2, 3, . . ., n, were necessary for ionisa- 
tion, and if the probability for each of them were ^^i, p^, ... , J^n, the 
ionisation would be proportional to the product pi,po,ps, ...,pn- 
We see from this, that if the probabiHty for the occurrence of one 
of the conditions is altered a certain number of per cent., the total 
amount of ionisation would be altered in the same proportion. 
Thus if the action of the pulse within a certain angle relative to 
some axis of the molecule were a necessary condition, the change 
in the probability of the occurrence of this condition would affect 
the total amount of ionisation proportionally. 

If now the rays had a continuous wave-front, we might be able 
to effect a detectable change in the probability of this condition. 
Suppose a cylindrical ionisation chamber is traversed by a beam 
of parallel rays perpendicular to the axis of the cylinder. If now 
we add another beam of rays traversing the same space of air 

Mr Vegard, An experwient on ionisation with y rays. 79 

inside the cylinder, we should get a different amount of ionisation 
according to the different angle between the two beams. Another 
way of putting it is to say, that the ionisation with such rays 
with a continuous wave-front would not be an additive property if 
the molecules had some axis of ionisation. 

For, as the wave-trains from one source in rapid succession 
traverse the chamber, these wave-trains would ionise those mole- 
cules that had a certain direction relative to the pulse, and if now 
a second source was applied with waves mainly in the same 
direction, a number of those molecules that otherwise would have 
been ionised by the second source are already picked up by the 
first one. 

2. It was from these considerations that I was led to undertake 
the following experiment, the object of which was to find whether 
the ionisation by 7 rays was strictly an additive property. 

Experiments on the additivity of ionisation have earlier been 
made by T. Noda*. In his experiments, however, the two sources 
gave rays of a different kind, and further one of his sources was 
radium giving out a mixture of rays, so that these experiments 
were of no use for deciding this question. 

Description of experiment. 

3. The ionising chamber had the form of a flat cylinder 
(length 4*9 cm., diam. 15"5 cm.). The ends of the cylinder were 
made of aluminium plates, the tube itself of a thin aluminium 
sheet. A circular aluminium plate was fixed inside the cylinder 
perpendicular to its axis by means of an aluminium rod connected 
to an electroscope of the Wilson type. The rod was surrounded 
by a guard-ring which was connected to earth, insulated from the 
rod by means of sulphur, and fixed to the chamber by a plug of 
ebonite. The wires leading to the electroscope were surrounded 
in the usual way by conductors connected to earth. 

The ionising chamber was placed with its axis vertical upon 
a small wooden bench fastened to the table. The 7 radiation came 
from two sources of radium ; one of them could be placed in a 
fixed position, the other on a moveable arm capable of rotating 
about a vertical axis coinciding with the axis of the cylinder. 
Thus the angle between the two bundles of rays could be altered. 
Each piece of radium was placed behind two slits formed by large 
lead blocks, in such a way that the radiation from each source was 
mainly restricted to the space between two parallel horizontal 
planes cutting the ionisation chamber at about equal distances 
(1 cm.) above and below the inner plate. The distances from the 

* T. Noda, Proc. of Camb. Ph. Soc. Vol. xiii. 1906, p. 356. 

80 Mr Vegard, An experiment on ionisation with <y rays. 

sources to the centre of the cylinder were about 35 cm. The 
a and ^ radiation was cut oif by lead plates 3 mm. thick. In all 
other directions the radiation was stopped by piles of large lead 
and iron blocks forming a layer about 5 inches thick around the 

The ionisation was measured by the saturation current between 
the inner plate and the chamber, the latter being given a potential 
sufficient for saturation when the inner plate had a potential 
nearly equal to that of the earth. The procedure was as follows : 

The air in the chamber was first exposed to the radiation from 
one source (a) alone, and the saturation current measured ; the 
second source (6) was then placed behind the second slit, while (6) 
was left unaltered, and the current measured ; then (a) was removed 
and the measurements repeated. This operation was performed 
for two different positions of the moveable source corresponding to 
the angles, 90° and 180°, between the mean direction of the ray 

The saturation current is inversely proportional to the time t 

required for the gold leaf to fall between the same two marks on the 

scale of the electroscope. This, however, is only true when there is 

no leak and the zero point corresponding to zero potential of the leaf 

remains constant. The leak observed when all radium was removed 

from the room was too large to be disregarded. The velocity of the 

gold leaf due to the leak was found for different positions of the 

leaf. From this the time T required for the leaf to move through 

the scale interval on account of the leak could be found. If the 

, . t' . 

time actually measured is t' , and if ™ is a small quantity, the time 

t, corrected for leak, will be - = t? + m- The leak might, however, 

Z V J- 

be altered by the presence of radium in the room ; by cutting off 
the rays that went directly to the chamber the leak could be 
estimated, and was found to be very little altered by the presence 
of radium. It is, however, not necessary to know this part of the 
leak, for we can assume that it is an additive property. 
The condition for additivity can then be written : 

i 1 l_J^ = o 

ta tb -^ tab 

In general this expression may be equal to some quantity e. 
The quantity S = tab'^ will then give a measure of the departure 
from additivity. 

The results of the measurements are given in the following 
table : 

Mr Vegard, An experiment on ionisation with <y rays. 81 

Part I. 











50 divisions 




50 „ 

50 „ 







+ 0,013 
+ 0,001 

- 0,002 

- 0,004 

Mean value 8 = + 0,0002. 

Part II. Angle 90°. 


40 divisions 
30 „ 
30 „ 











+ 0,001 

Mean value 8 = - 0,003. 
The time is given in minutes. 

The table shows that within the limits of experimental error 
the ionisation of air with y rays is strictly an additive property, 
and that, as far as the effect sought for is concerned, the experi- 
ment has given a negative result. In view of the previous 
considerations the result only shows that at least one of the two 
conditions necessary for the effect must be wanting; but apart 
from its connection with the previous considerations the result is 
of interest in itself, as giving a property characteristic of ionisation 
with 7 rays. 

82 Mr Piirvis and Miss Homer, The absorption spect7'a of 

The absorption spectra of solid tetramethylpicene and of its 
solutions. By J. E. Purvis, M.A., St John's College, and Miss A. 
Homer, Fellow of Newnham Colleg-e. 

[Bead 8 February 1909.] 

From the products of the action of aluminium chloride on 
naphthalene investigated by one of us (Homer, Trans. Chem. Soc. 
1907, vol. xci. p. 1103) there was isolated a new hydrocarbon whose 
empirical formula was CosHno. It was suggested that this sub- 
stance was an alkyl derivative, probably tetramethyl, of dinaphth- 
anthracene, CooHi^. 

In a later paper by the present authors (Homer and Purvis, 
T7'ans. Chem. Soc. 1908, vol. xciii, p. 1319), it was thought that 
further evidence as to the constitution of this hydrocarbon might 
be obtained from a comparative study of the absorption spectra of 
its solutions with the spectra of solutions of the supposed parent 
substance, dinaphthanthracene, and of picene the isomeride of 
dinaphthanthracene. Benzene solutions of these hydrocarbons 
were compared because picene and dinaphthanthracene are practi- 
cally insoluble in alcohol. As a result of the investigation it 
was found that the absorption curve of the hydrocarbon CseHgs 
exhibited the same type of curve as picene, and therefore the 
substance was considered to be an alkyl derivative of picene. 

Some comparative experiments were conducted about the same 
time, both with solutions in alcohol and in benzene, with the 
solid and with the vapour of the hydrocarbon CogHos. With 
regard to the solutions, A7IOOO solutions in benzene and in alcohol 
were taken and the absorption curves plotted in the same way 
as is described in the previous paper {loc. cit.). The solid 
hydrocarbon CobH^ liquefies at 49 — 50° C, so that it was quite 
easy to melt a little of the substance on microscopic glass cover- 
slips, by which a ver}^ thin layer was uniformly spread over the 
surface of the glass : the layer was quite translucent. The glass 
was then clamped before the slit of a spectroscope and the light of 
a Nernst lamp, of an iron arc, and of a condensed iron spark were 
used as the sources of light. Photographs were taken of the 

solid tetramethylpicene and of its solutions. 83 

resultant absorption spectrum and they were compared with the 
absorption spectra of the benzene and alcoholic solutions. It was 
found that in the three series of experiments the substance showed 
three absorption bands, but that the relative position of the bands 
varied. The bands of the solid were moved more towards the red 
end of the spectrum than those of the alcoholic solution, whilst 
their positions in the benzene solution were between those of the 
solid and the alcoholic solution. In order to compare the results 
the following table gives the numbers of the three bands in terms 
of the mean oscillation frequencies : 

C^U,,, solid 2264 2405 2537 

i\^/1000 benzene solution 2290 2424 2584 
i\^/1000 alcoholic „ 2304 2441 2590 

The numbers for the benzene solution are extracted from the 
before-mentioned paper by Homer and Purvis (loc. cit). And 
comparing the positions where general absorption begins the 
numbers are: 

C26H22, solid 2182 

benzene solution 2212 
alcoholic „ 2247 

It is evident from these numbers that there was a shift in the 
position of the bands and of the general absorption towards the 
red end of the spectrum according to the density of the medium, 
whilst in the solid state the shift was more marked still. 

The rate of vibration of the molecules of the solute must be 
affected by the molecules of the solvent, that is to say the more 
dense the medium the greater damping effect will it have on the 
rate of vibration of the dissolved molecules. 

Now in the solid state the mean free path of the molecules is 
more restricted than when they are distributed throughout some 
solvent, therefore the rate of vibration of the molecules of the 
substance in the solid state should be slower than when in 

Assuming that the general absorption is due to the vibrations 
of the molecule and that the selective absorption is caused by 
intra-molecular vibrations of the atoms which are also affected by 
the molecular vibrations, then conditions which tend to damp the 
rate of the molecular vibrations, that is, which cause a shift in the 
general absorption will also cause a corresponding shift in the 
selective absorption of the substance. 

The results obtained are in accordance with this view, for a 
comparison of the positions of the general and selective absorption 
of the hydrocarbon in alcoholic and benzene solutions and in the 
solid state shows that for benzene solutions there is a shift towards 

84 Mi' Purvis and Miss Homer, The absorption spectra, etc. 

the red end, and that this shift is more marked still for the 
absorption bands of the solid hydrocarbon. 

Endeavours were also made to observe the absorption spectrum 
of the vapour of the hydrocarbon. For this purpose a small 
portion of the solid was placed in a thick hard glass bulb of about 
50 mm. diameter. The bulb was then exhausted of air and placed 
in a special apparatus designed to heat the bulb equally in all 
directions so that the density of the vapour would be the same at 
every point. The light of an iron arc or of a condensed ii'on spark 
was used for different observations, but it was found that the 
hydrocarbon decomposed so rapidly that no results were obtained. 
The vapour of the hydrocarbon exhibited a most beautiful blue 
fluorescence, very intense at first but rapidly becoming weaker. 
The decrease in fluorescence seemed to be proportional to the 
decomposition of the hydrocarbon, as evidenced by the conversion 
of the substance to a brownish tarry residue. The decomposition 
may have been started either by the action of the small amount of 
air left in the bulb or by the contact action of the heated glass. 

We hope to continue the work on the absorption and fluorescent 
spectra of the vapour of this and of other hydrocarbons. 

Mr Purvis, The absorption spectra, etc. 85 

The absorption spectra of concentrated and diluted solutions 
of chlorophyll. By J. E. PuRVis, M.A., St John's College. 

[Read 8 February 1909.] 
(Plates I— III.) 

The general phenomena of the absorption spectra of solutions 
of chlorophyll have been described by various observers, and refer- 
ences to such work up to 1908 are included in Kayser's Handbuch 
der Spectroscopie, vol. IV. But, so far as the author knows, there 
are no recorded observations on the comparative spectra of equiva- 
lent quantities of chlorophyll in strong and dilute solutions : and 
the aim of this paper is to describe a series of observations which 
have been made in this direction. 

The well-dried leaves of fresh parsley were ground to a powder, 
and the chlorophyll extracted with rectified spirit, filtering the 
insoluble portions. A portion of the strong solution was diluted 
7 19 "8 times with rectified spirit, and the strong solution was 
placed in a glass cell of 5 mm. internal width, whilst the diluted 
solution was introduced into a glass tube, with glass ends, 3599 mm. 
long. The ratio of the dilutions was, therefore, as 1 : 719*8, and 
there was as much chlorophyll in the one solution as in the other. 
The two solutions were exposed to the same source of light for 
equal periods of time. The only alteration in the conditions was 
that made necessary by the change of the small cell with the 
strong solution for the long tube with the dilute solution; with 
this exception, all the conditions were fixed and exactly the same 
throughout the whole series of observations. The apparatus and 
photographic spectroscope used for the observations have been 
fully described in the Proc. Camb. Phil. Soc. vol. xii. pt. III. p. 206, 
in some experiments by the author on the absorption spectra of 
concentrated and diluted solutions of didymium and erbium salts. 

Description of photographic plates. 

Unfortunately, it has not been found possible to reproduce the 
phenomena observed on the original photographs with any close 
degree of precision. The fault is particularly noticeable in the 
weak band \ 565, which is unmistakeably clear on the original 
photographs. The gradual changes, however, can be traced fairly 
closely by comparing the changes of the bands X 538 and A, 508 
in the reproductions 1 to 9, and which are described in the cor- 
responding paragraphs 1 to 9. 

86 Mr Purvis, The absorption spectra of 

1. These photographs were taken immediately after the 
solutions were made. In both solutions the bands at \ 538 and 
X565 are of the same width and intensity. The X565 band is 
very weak in the reproductions, but it is quite visible in the 
original photographs. The general absorption in both begins at 
about A, 510. 

2. The second series of photographs were taken after the 
solutions had been standing for some hours. The band \538 in 
the dilute solution is more diffuse and weaker than the band in the 
strono- solution ; otherwise there is no chancre in the two solutions. 

3. After standing twelve hours longer, the bands \ 538 and 
X565 appear to be very like the last photographs. But in the 
strong solution a faint band X508 has appeared, which is not 
visible in the dilute solution. 

4. After standing twelve hours longer, the concentrated solu- 
tion shows that the bands X 538 and X565 are very like those in 
the last observations : whilst the band X 508 is more clearly 
marked. In the diluted solution, the bands X 538 and X 565 are 
still weaker and more diffuse than the corresponding bands in the 
strong solution, and X538 is particularly noticeable in this respect. 
There is no band at X 508 in the diluted solution corresponding to 
that in the strong solution. 

5. After standing twelve hours longer, the general appearance 
of the bands is much the same as in the last series of observations. 
But in the strong solution there is a gradual increase in the amount 
of light coming through on the more refrangible side of the band 
X 508 ; and there is no such appearance in the diluted solution. 

6. The solutions wei'e allowed to stand four days longer. In 
the strong solution the bands X 565, X 538, and X 508 are like those 
in the last series of observations. In the dilute solution the band 
X 538 is weaker and more diffuse than the corresponding band in 
the strong solution. The latter band is as well marked as at the 
beginning of the observations. In the strong solution the band 
X 508 is noAv well marked, and is absent in the dilute solution. 
Besides that, there is less general absorption of light by the strong 
solution than the. dilute solution. 

7. The solutions were allowed to stand tw^o days longer. The 
general appearance of the phenomena of the two solutions is very 
similar to that in the last series of experiments. 

8. After standing four days longer, photographs were again 
taken, and they showed that the bands were very similar to those 
in the last series of experiments ; but the general absorption in 
the strong solution was less than before, whilst that in the dilute 
solution does not appear to have altered. 

9. Finally, after standing fourteen days longer, the photo- 
graphs show that in the strong solutions the bands X 538 and X 508 

Plate I. 

Dilute solution 

Strong solution 

Strong solution 

Dilute solution 

Dilute solution 

Strong solution 

Plate II. 

strong solution 

Dilute solution 

Dilute solution 

Strong solution 

Strong solution 

Dilute solution 

Plate III. 

Dilute solution 

Strong solution 

Strong solution 

Dilute solution 

Strong solution 

Dilute solution 

concentrated and diluted solutions of chlorophyll. 87 

are quite well marked : there are very faint traces of the band 
\ 565, and the general absorption has decreased very considerably. 
In the dilute solution the band A, 565 is stronger, and the 
band A, 538 is much weaker and more diffuse than the correspond- 
ing band in the strong solution, and, in fact, it has almost dis- 
appeared. In the dilute solution no band at X 508 appeared. 
There is also a gradual creeping in of light on the more refrangible 
side in the dilute solution when compared with the last series of 
observations. The difference between the general absorption at 
the beginning (1), and at the end of the observations (9), in the 
dilute solutions is very small, whilst that of the strong solution is 
very striking. 

Discussion of the results. 

As no effort was made to purify the chlorophyll, it is probable 
that some vegetable acid was present : and, by the continued use 
of the alcoholic solutions, a little of the spirit may have been 
oxidised to acetic acid : for, at the end of the experiments, the 
solutions were found to give a weak acid reaction with litmus 
paper. In any case, the first series of photographs showed absorp- 
tion spectra very similar to those described by Russell and 
Lapraik (Jour. Ghem. Soc. vol. XLI. (1882), p. 334). Their solutions 
were obtained by the action of very dilute acids on fairly pure 
chlorophyll. Assuming, therefore, that the solutions used in these 
experiments show absorption bands characteristic of chlorophyll 
solutions in the presence of a very small amount of acid, some 
explanation is necessary to account for the gradual changes in the 
bands and the general absorption of two solutions containing equal 
amounts of chlorophyll, one of which was diluted 719 times that of 
the other. 

(1) The greater volume of the diluted solution might have 
contained sufficient dissolved oxygen to oxidise the small quantity of 
the dissolved chlorophyll. Against this argument is the fact that 
although both solutions stood for several weeks in a well-lighted 
room and with easy access of air, the changes in the strong solu- 
tion were not in the same direction as those in the dilute solution. 
It was the dilute solution which showed more general absorption 
at the end of the experiments. If the primary cause of the changes 
had been oxygen, the dilute solution might have been expected to 
have undergone a greater change. 

(2) The changes might have been caused by the action of a 
very weak acid analogous to that which occurs by the decomposi- 
tion of sugars and glucosides, whereby complex molecules are broken 
down into simpler ones ; but the same objection may be brought 
against this explanation as against the last. 

VOL. XV. PT. II. 7 

88 Mr Purvis, The absorption spectra, etc. 

(3) It is more probable that the changes may have been 
produced by the differentiating effect of enzymes, like the 
oxydases, dissolved from the parsley with the chlorophyll, some 
of which are known to be very soluble in rectified spirit. In the 
concentrated solution the enzymes would be in more intimate 
contact with the chlorophyll than in the dilute solution, and 
the consequent break down of the chlorophyll molecule would be 
sooner effected. This suggestion would explain the less general 
absorption of the strong solution than of the dilute solution after 
they had been standing for some time, as well as the changes 
in the appearance and position of the bands, although the 
substances corresponding to the bands \ 588 and A, 508 do not 
appear to have suffered much change in the strong solution. 

(4) It is hardly likely that the dissociating force of the 
solvent was a factor in the changes. The system was too complex 
to explain them by this theory, for there was not only chlorophjdl 
in solution, but also, most probably, small quantities of other 

The dissociating effect of the solvent on some dyes may be 
mentioned in connection with the above-mentioned changes in the 
chlorophyll solutions. For example, strong aqueous solutions of 
dyes like eocine and magenta, when diluted in the same way as 
chlorophyll, gradually and slowly lose their brilliant colour whilst 
the strong solutions retain it. But the colours of the dilute 
solutions are at once restored by a single drop of an acid like 
hydrochloric acid, and there is no such reversion in the dilute 
chlorophyll solution ; so that the changes produced by dilution of 
the dyes are not comparable with those of the chlorophyll solutions. 

Mr Purvis, The absorption spectra of mesitylene, etc. 89 

Tlie absorption spectra of mesitylene and trichloromesitylene. 
By J. E. Purvis, M.A., St John's College. 

[Read 8 February 1909.] 

The absorption spectrum of mesitylene in the ultra violet region 
has been described by Hartley and Huntington (Phil. Trans. 
vol. CLXX. (1879), pp. 257 — 274). They noted a band between 
A, 27 5 — A- 245 in strong solutions. By diluting this solution in 
the ratio of 1 : 2000, the strong band is resolved into three small 
sharp bands, which remain visible in a solution of 1 : 8000. 

Drossbach {Ber. Chem. Ges. vol. xxxv. (1902), pp. 1486—1489, 
noted that general absorption occurred at A, 336, but this occurs 
only in a very thick layer. He did not appear to have noticed 
any bands. 

Coblentz (Astrophy. Jour. vol. xx (1904), pp. 207—223), has 
observed the presence of a considerable number of bands and lines 
in the ultra red. 

The author has compared the absorption spectrum of trichloro- 
mesitylene with that of mesitylene, when equivalent quantities of 
substances were in alcoholic solutions. He noticed that the bands 
and the general absorption were shifted in the trichloromesitylene 
more towards the red end of the spectrum when compared with 
their positions in the mesitylene solution. For example, through 
a thickness of 40 mm. of solution and iVyiOOO concentration the 
strong band in mesitylene lay between \ 269 — \ 254, whilst that of 
the trichloromesitylene was between \ 287 — A, 263. Also, a most 
important difference was the greatly increased persistence of the 
absorption curve of the trichloromesitylene as compared with that 
of the mesitylene. The loading of the ring by the chlorine atoms 
influenced the vibration of the molecule so that the absorption 
band was shifted towards the red end of the spectrum and agrees 
with the effect previously observed by Hartley in the case of 
substituted compounds, and, at the same time, the persistence of 
the band was greatly increased. 

It has been shown by Baker and Baly {Jour. Ghem. Soc. 
vols. xci. and xcii. p. 1122), that, in bhe case of pyridine, the intro- 
duction of chlorine atoms into the nucleus not only shifted the 
bands towards the red, but also greatly increased their persistence, 


90 Mr PiD-ms, The absorption f^pccfra of mesitylene, etc. 

and the explanation was that such an introduction reduced the 

residual affinity of the nitrogen atom, and thereby allowed greater 
freedom of vibration or pulsation of the ring. 

The author has pointed out in previous communications 
{Proc. Gamh. Phil. Soc. vol. xiv. (1908), pp. 881, 435 and 568) 
that the persistency of the band in pyridine compounds is con- 
ditioned to a considerable extent by the relative or spatial 
positions of the introduced chlorine atoms as well as by their 
introduction either in the nucleus or the side chains. 

Now the increased persistence of this strong band of trichloro- 
mesitylene is very similar to that of the chlorine compoiuids of 
pyridine and several of its methyl derivatives, where the chlorine 
atoms had entered the nucleus, and, unless we assume some 
changing valency of the atoms of the benzene ring, it does not 
seem easy to correlate the two series of phenomena. 

But before any definite conclusion can be drawn from these 
observations on mesitylene and trichloromesitylene, it will be 
necessary to examine the absorption spectra of other chlorine 
compounds of the former substance, both when the chlorine atom 
or atoms are in the nucleus and when they are in the side chains. 

All that can be said at the present stage of the investigation 
is that (1) the strong absorption band of the trichloromesitylene is 
shifted more towards the red end of the spectrum than the corre- 
sponding band of mesitylene, and that (2) the persistence of the 
band of the former compound is much greater than that of the 

Mr W. H. Foster, of St John's College, was good enough to 
make up the solutions of the two substances examined. 

Mr Dobell, On a so-called "sexual" method of forming spores, etc. 91 

On a so-called "sexual" method of forming spores in Bacteria. 
By C. C. Dobell, B.A., Trinity College. 

[Read 22 February 1909.] 

Two species of Bacteria — Bacillus butschlii (Schaudinn) and 
B. flexilis(Dohe\l) — are known which differ from all other Bacteria 
in forming two spores instead of one in each cell. Before spore- 
formation, the following remarkable phenomena are to be seen : 

A large individual begins to divide into two, but the division 
is never completed, and all signs of it are subsequently lost. The 
granules (? chromatin) in the cell then show streaming movements, 
arrange themselves in the form of an irregular spiral in the long 
axis of the cell, and finally heap themselves up at both ends of the 
organism to form the two nucleus-like spore-rudiments. Round 
each of these, a spore membrane is formed, so that the two spores 
when fully formed lie at opposite poles. 

The process of incomplete division and subsequent fusion im- 
mediately preceding spore-formation were considered by Schaudinn, 
and also by myself, to represent a form of conjugation such as is 
found in some yeasts, Heliozoa, etc. — that is to say, a conjugation 
of sister-cells. 

From further investigations upon Bacillus spirogyra, Bacterium 
lunula n.sp. and other Bacteria, it now appears to me to be certain 
that no " sexual " process really occurs in the disporic Bacteria. I 
believe that what has really happened is that the last bipartition 
in the life-cycle — the one immediately preceding spore-formation — 
has become abortive, and is not as a rule completed. The disporic 
individuals are therefore really double individuals — physiologically, 
but not morphologically. 

If this interpretation of the phenomena is correct, then it has 
some interesting results : for instance, it has an important bearing 
upon the problem of the affinities of the Bacteria. One of the 
most important arguments in favour of the close relations of 
Bacteria and yeasts is removed. It has also some significance 
with regard to the problem of " sexuality " in the Protista and in 
living beings generally. 

A discussion of these problems, and also of some special points 
{e.g. the nucleus of B. spirogyra, etc.), will be given in my full 
account of this matter, which I hope to publish before long in the 
Quart. Journ. Microsc. Sci. 

92 i)f?' Pimnett, On the alleged influence of lecithin 

On the alleged influence of lecithin upon the determination of 
sex in rabbits. By R. C. Punnett, M.A., Gonville and Caius 

[Bead 22 February 1909.] 

In 1907, Professor Russo, of Catania, published an account of 
certain experiments* in which he claimed to have brought about 
a great increase in the relative number of female young produced 
by rabbits. The method consisted in the injection of lecithin 
either subcutaneously or into the abdominal cavity. In the paper 
referred to Russo gives particulars of 100 litters from injected 
does as well as of another 100 litters in which the does were not 
injected. The injected does produced 217 (^(^ and 431 ? ?, 
as against 400 </</ and 287 $ $ from those not treated, and the 
author consequently claims to have raised the proportion of 
females from 41'8 °/^ to 56'5 % o^ the total offspring. 

Such remarkable results have naturally attracted attention 
and several criticisms have recently appeared. It has been pointed 
outf that the statistics published by the author are not complete, 
but that, as he himself states, only those litters from the animals 
treated with lecithin were recorded in which the number of females 
preponderated over that of males (cf. Russo, loc. cit. p. 367, foot- 
note). Until the complete statistics are available, any conclusions 
as to the effect of lecithin upon the proportions of the sexes must 
necessarily be of doubtful value. 

On other grounds Russo's results have been recently criticised 
by Heape|. Russo claimed to have distinguished histologically 
between the ovarian ova destined to produce females and those 
destined to give rise to males. According to him fatty matter is 
present in the former though not in the latter, and he supposed 
that the injection of lecithin resulted in a higher proportion of 
ova containing fat, i.e. of female ova. Heape points out that there 
are good grounds for regarding Russo's male ova as ova which are 
in some stage of degeneration and consequently not destined to 
give rise to embryos of either sex. 

* Atti Acad. Lincei, 1907, Serie 5 a. Vol. vi. pp. 313—384. 
t Bateson and Punnett, Science, N.S., May 15, 1908. 
+ Proc. Camh. Phil. Soc, Vol. xiv. p. 609. 

upon the determination of sex in rabbits. 93 

During the past year Russo's experiments have been repeated 
by Basile* with negative results. From six injected does he had 
117 young in 17 litters, and of these 66 were (/cf and 51 were 
$ ? . He also bred 60 litters from nine rabbits which were not 
injected, and of the 440 offspring 225 were (/*(/ while 215 were 
$ $ . Among the offspring of the uninjected the proportion of 
females was actually slightly higher than among the injected. 

Being desirous of repeating Busso's experiments I wrote to 
him in February, 1908, asking for certain details in his method. 
He very kindly sent me the information for which I had asked, 
and at the same time informed me that he had produced similar 
results by feeding with lecithin in place of the injection. My 
experiments were carried out in accordance with the details of the 
feeding method of which he sent me particulars. An emulsion 
was prepared by shaking up 5 grams of lecithin (Merck) with 
1000 c.c. of physiological salt solution ('65 %). The daily dose for 
each rabbit was 20 c.c. of this emulsion made up into a paste 
with meal, and the treatment was continued for three months 
before the doe was put to the buck-f-. I also went on with it for 
a few days subsequent to this. No difficulty was experienced in 
getting the rabbits to take their daily dose, for they soon became 
exceedingly fond of it and ate it greedily as soon as it was offered 
them. During the past summer 10 does were treated in this way, 
and they eventually produced between them 47 young. Of these 
24 were ^f^ and 23 were $ $ . From these and other does not 
treated with lecithin I have had 18 litters with 103 young, and of 
these 54 were (/(/ and 49 were $ $ . In either series of experi- 
ments the numbers are not large, but so far as they go they are 
entirely opposed to the view that feeding on lecithin has any 
influence on the relative proportion of the sexes among rabbits. 

* Atti Acad. Lincei, 1908, Vol. xvii. 1, p. 643. 

t Here I would express my thanks to my friend Mr F. A. Potts for kindly feeding 
the rabbits for me during a week when I was absent from Cambridge. 

94 Messrs Jones and Tasker, A coloured thio-oxalate. 

A coloured thio-oxalate. By H. O. Jones, M.A., Clare College, 
and H. S. Tasker, B.A., Emmanuel College. 

[Read 8 February 1909.] 

In investigating the action of substances on oxalyl chloride, 
(C0C1)2, in the hope that chlorine might be removed and C2O2 be 
produced, thiophenol and its metallic compounds were used, since 
the easy formation of diphenyl disulphide renders these substances 
good reducing agents. 

Sodium thiophenolate reacts violently with oxalyl chloride, but 
in place of C2O2 two molecules of carbon monoxide are produced. 

The action of thiophenol itself is less violent. On mixing 
equivalent quantities of oxalyl chloride and thiophenol a yellow 
colour is immediately produced and hydrogen chloride is evolved. 
The evolution of gas continues until the mixture finally sets to 
a solid mass. By crystallization from ether long sulphur-yellow 
prisms are obtained, melting at 119 — 120° C. The substance 
distils unchanged at atmospheric pressure. 

On treatment with aqueous potash the substance dissolves, 
giving in solution potassium thiophenolate and potassium oxalate, 
the colour disappearing. 

This behaviour, coupled with the mode of formation, indicates 
that the substance is diphenyl-dithio-oxalate, formed according to 
the equation 

2C6HbSH + (COCIX = (COSCeHs)^ + 2HC1. 

On combustion '2857 gms. of the substance gave '6402 gms. of 
CO2 and -0951 gms. of H^O. 

Observed percentages C 61*12 H 3"70. 

Calculated for diphenyl-dithio-oxalate C 61"31 H 8"85. 

The substance is the first member of the class of dithio-oxalates, 
and is interesting by reason of its colour (which is undiminished 
by heating in ethereal solution with animal charcoal or by repeated 
recrystallization), since diphenyl oxalate and monothioxalic esters 
are colourless, while glyoxal is yellow. 

Messrs Jones and Tasker, A coloured thio-oxalate. 95 

In order to see if C2O2 could be obtained as the result of 
decomposing this substa,nce, it was heated in an evacuated vessel 
with metallic sodium. The resultant gas was collected by means 
of a Sprengel pump. There was a sudden rush of gas, in quantity 
far short of the theoretical, and some deposition of carbon. The 
gas was insoluble in water or potash but was soluble in cuprous 
chloride and burnt with a blue flame. Its vapour density was 
taken by weighing a known volume. It corresponded with that 
required for carbon monoxide. 

94-24 c.c. at 654 mm. and 16° C. weighed -1002 gms. 
Vapour density (H = 1) 14'5 
Theory for CO 14 

With concentrated sulphuric acid, carbon monoxide is again 
given off and a purple colour is given which is characteristic of the 
behaviour of diphenyl-disulphide under the same conditions. 

Other coloured esters and several metallic salts of dithio-oxalic 
acid have been prepared, and their properties and derivatives are 
being investigated. 

96 Mr Potts, Observations on the changes 

Observations on the changes in the Common Shore- crab 
caused by Sacculina. By F, A. Potts, M.A., Trinity Hall. 

[Bead 22 February 1909.] 

Professor Alfred Giard, whose recent death all zoologists must 
deplore, established a great reputation by the brilliance and versa- 
tility of his researches. Perhaps his most noteworthy discovery 
w^as that the Rhizocephala, a family of aberrant parasitic Cirri- 
pedes, produce an extraordinary modification of the sexual 
characters of the Decapod Crustacea they infect*. The evident 
results of the association are the dwindling of the reproductive 
glands of the host and the effacement of already existing secondary 
sexual characters (such as copulatory styles) and assumption of 
those of the other sex. 

Since Giard wrote, the nature of these effects has been clearly 
set forth by Geoffrey Smith f for the case of the spider-crabs 
(Brachyura oxyrhyncha). Perfect sterility and the disappearance 
of the gonads results. The abdomen of the male becomes trough- 
shaped, often completely resembling the female type. The first two 
abdominal appendages modified as copulatory styles dwindle, and 
on the other segments a varying number of swimmerets, charac- 
teristic of the female, are developed. Modification in the converse 
sense is not observed in the female, but that of the male evidently 
indicates the development of a hermaphrodite condition : for male 
crabs, which have undergone these changes, freed from the para- 
sites and allowed to recover, may regenerate an ovotestis with 
mature sexual products of both kinds. 

This, then, is an example of extreme modification. The common 
shore-crab {Carcinus moenas) when attacked by the same parasite 
offers a case of slight or incipient modification. The short descrip- 
tion we owe to Giard is vague on several important points, and 
the common association of the shore-crab and Saccidina on our 
own coasts;]:, also renders it desirable that another account of the 
phenomenon should be given. 

* "La Castration Parasitaire, " Bull. Sc. Dep. Nord. Ser. 2, Tome xviii. 1887, 
p. 1, and Ser. 3, Tome i. 1888, p. 12. 

t "Ehizocephala," Mon. 29, Fauna u. Flora des Golfes von Neapel, 1906. 

X In Plymouth Sound a considerable proportion of the shore-crabs are found to 
harbour Saccidina. It is curious to note that in many localities, e.g. Liverpool 
Bay and the Isle of Man, the parasite is rarely or never found. 

in the Common Shore-crab caused by Sacculina. 97 

In the first of two papers on " La Castration Parasitaire " 
Giard mentions the fact that a certain alteration in the character 
of the abdomen can be noticed in male shore-crabs attacked by 
Sacculina. The diagrams which he gives show plainly that the 
infected males often possess an abdomen broader than that usually 
associated with this sex, yet not attaining the full trough-like 
development of the female. It was Giard's view that the female 
might approach the male type when parasitised ; he does not here 
however refer to any modification of the female. Though no 
definite statement is made the reader of this paper is led to 
assume that atrophy of the gonads takes place. 

To understand the account of the changes in the sexual 
characters, certain particulars of the life history need to be supplied. 
The elucidation of the extraordinary development of Sacculina 
is found in a brilliant paper by Delage*. The fertilised eggs 
develop into free swimming Nauplius larvae. These fix at the 
base of hairs on the carapace of crabs, and the almost disorganised 
mass of cells which has resulted from histolysis of the larval body 
passes through the gap in the carapace which the articulation of 
the hair affords. It wanders through the body cavity, and even- 
tually becomes attached to the intestine in the region of the 
abdomen. Here it grows, absorbing nutriment from the blood, 
and attains to the development of the adult parasite. The in- 
ternal stage of development is terminated by a moult. For if 
the Sacculina is ripe for emergence it is found that the part of 
the parasite destined to become external has eaten its way through 
the muscles and epithelium of the abdominal wall of the host and 
when the chitinous exoskeleton is cast, this visceral mass emerges. 
Connection with the internal root-system is maintained by the 
narrow peduncle occupying the aperture which served for escape. 

In crabs (Brachyura) the abdomen is clothed with a fairly 
thick exoskeleton. It follows that when the new shell is formed 
after the moult described above the Sacculina acts as a rivet and 
prevents the fleshy part of the abdomen, in any subsequent 
attempt at moulting, being withdrawn from its chitinous case. 
The fact that a crab infected by Sacculina is prevented from 
further moulting and consequently from growth after the parasite 
becomes external is well known, but I consider it to be due to the 
mechanical disability, which I have pointed out above, alone. It 
might conceivably be a repression of growth occasioned by the 
drain of nutriment for the parasite or the action of some specific 
substance secreted by that organism. But if this were so we 
might expect to find a tendency to inhibit the moult which intro- 
duces the Sacculina to the external world, also at work. For 

* Arch. Zool. Exp., Ser. 2, Tome ii. 1884, p. 417. 


Mr Potts, Observations on the changes 

while the parasite is in its internal stage the change occurs which 
finds expression in the modification of the secondary sexual 
characters in the new carapace. If a change of this magnitude 
can be induced in the early stages of parasitism we might also 
expect that the effect on growth and moulting would be established 
and the SaccuUna prevented from ever appearing at the exterior. 
There does not appear to be any evidence for infrequency of 
moults in crabs with Sacculina interna. It may here be pointed 
out that the hermit crab when attacked by Peltogaster* (a near 
relative of Sacculina) still moults regularly, a fact we can easily 
trace to the investment of the abdomen by soft skin which tears 
easily and so detaches itself in moulting, round the base of the 
parasite. The degree of modification produced in this case is 
great, but Peltogaster does not mechanically prevent the shedding 
of the exoskeleton, and growth appears even to be favoured by 
the presence of the parasite. 

The general nature of change in the secondary sexual characters 
has already been indicated. The increase in the width of the 
abdomen is exemplified in the following diagrams similar to those 
which accompany Giard's paper. It will first be noticed that 

Modified male. 


while all the segments of the female abdomen are freely moveable, 
in the male the third, fourth and fifth are fused together. The 
first evidence of modification in the infected male is the re- 
established segmentation of the abdomen. 

The degree of modification may be actually measured by 
estimating the ratio of the breadth of the abdomen at the segment 

in Fig. ) . The indices so given are as follows : 

to the length , ^^ 

Uninfected male crab '57 — 'oS 

Uninfected female crab *90 

Infected male crab which has suffered the maximum 
amount of modification '77 

Q. J. Microsc. Sc, Vol. l. 1906, p. 599. 

in the Common Shore-crab caused by Sacculina. 99 

The male crab with the largest index does not approximate 
very closely to the female type, and those so markedly modified 
are but a small proportion of the whole. A third of the crabs 
measured could be called entirely unmodified, a proportion which 
corresponds roughly with the quarter unaffected by the parasite 
in the case of the spider-crab, and of the hermit-crab. 

The number of crabs measured was 59, so that the series is 
too small to be satisfactorily plotted in the form of a curve. Some 
idea of the distribution may be gained by the statement that 
37 possessed an index between "56 — '66, while that of the re- 
maining 22 lay from "67 to '77. In the first group there were 
11 wdth an index of "60, and in the second 5 with one of "72. 

One point in Giard's short account which I desired to test was 
his assertion that the older (or larger) crabs were not subject to 
modification. The average carapace breadth of the crabs of index 
•56 — '66 to be sure is 4*9 as compared to 4*5 of those from 
•67 — ^77, but the figure for the index -72 is 4-6 and for -77 the 
extreme limit of modification is 4"7. Occasional crabs of excep- 
tional size are met with, with abdomina considerably broadened, 
and my observations give practically no support even for the 
statement that younger crabs are more liable to modification than 
older individuals. 

In the abdomen the effect of the parasite was distinctly less 
than is the case with the spider-crabs. With the other secondary 
sexual characters no alteration was experienced. There was no 
diminution of the copulatory styles in size and no appearance 
of the abdominal swimmerets which are characteristic of the 

In the female no change was ever detected in the abdomen as 
a result of parasitism, and the swimmerets appeared fully as 
well-developed and thickly fringed with hairs as in crabs free 
from the Sacculina. 

With regard lastly to the sexual glands of the infected shore- 
crab, here again there is little alteration. The females never bear 
eggs, and the ova in the ovary are as a rule small and white, and 
devoid of great stores of yolk. In the uninfected male the testes 
are lobulated organs, stretching on each side across the liver. 
The development varies greatly even in normal specimens. The 
vasa deferentiae follow, and speedily become wide tubes with a 
very characteristic milky white appearance, due to the multitude 
of spermatophores, each crammed with spermatozoa, which they 
contain. Posteriorly the male duct opens on the terminal joint 
of the last thoracic leg, at the end of a long fleshy penis. 

In infected males a certain diminution in size of the testis is 
often noticeable, but actual atrophy never takes place. There is 
very little reduction in size of the vasa deferentiae, and they always 

100 Mr Potts, Observations on the changes, etc. 

preserve the normal appearance, containing spermatophores in 
large number with ripe spermatozoa. The genital aperture is 
never blocked up with chitin as occurs in the cases of extreme 
modification, and the penis shows no tendency to disappear. In 
fact it is quite clear that the effect on the reproductive glands is 
only small — the most noticeable change being the failure of the 
female to produce large heavily-yolked eggs. The male, it might 
be supposed, could impregnate the female successfully were it not 
that the presence of the Sacculina prevented copulation. It would 
be interesting to observe whether infected males ever attempt the 
sexual act. 

In summarising emphasis must be laid on the low grade of 
the modification. One organ only, the abdomen, is subject in the 
male to a change of a rather striking nature, though the testis 
continues to produce spermatozoa and the ducts to be filled with 
spermatophores. It may be pointed out that the term " castration 
parasitaire," as applied to the phenomenon by Giard, is somewhat 
misleading here as in other cases, for the modification of the 
secondary characters is not associated with the suppression of 
the gonads. 

In Pachygrapsus marmoratus, the common shore- crab of the 
Bay of Naples, another of the numerous hosts of Sacculina, the 
modification of the abdomen of infected males is of the degree 
described above, i.e. about half-way between male and female types. 
In other respects the change is far greater than that in Garcinus. 
The female swimmerets appear on the abdomen in more or less 
complete sets (no mention is made of diminution of the copulatory 
styles), and the gonads are greatly reduced and may entirely dis- 
appear. The case of Carcinus is better compared with that of the 
" stylopised" males of bees {Andrena)* which undergo considerable 
external change, though throughout parasitism the testis of one 
side remains fully developed, and produces spermatozoa. 

* Perez. Mem. Soc, Bordeaux, T. iii. 1880, p. xlii. 

Mi^ Growther, On the secondary Rontgen radiation, etc. 101 

On the secondary Rontgen radiation from air and ethyl 
bromide. By J. A. Crowther, M.A., St John's College. 

[Read 25 January 1909.] 

In a previous paper* I have shewn that certain gases and 
vapours, and notably compounds containing arsenic or bromine, 
give off amounts of secondary Rontgen radiation enormously 
greater than that given off by air under similar conditions. Thus 
the ionization produced in air by the secondary rays from ethyl 
bromide is some 540 times greater than that produced by the 
rays from air itself under similar circumstances. The rays from 
ethyl bromide are much softer than those from air, and in a 
recent paper Prof Braggf has siaggested that in this fact may 
lie a possible explanation of what he describes as the " startling 
results obtained in the case of arsenic and bromine." He points 
out that the rays from an ordinary X-ray bulb are hard to sub- 
stances of low atomic weight such as aluminium or air, but soft to 
the elements of higher atomic weight such as copper or iron. The 
secondary rays from air are of the same type as the primary rays. 
The secondary rays from bromine however are of a much softer 
character, and so, to quote Prof Bragg's paper, " are brought 
within reach, so to speak, of air, which rapidly converts them into 
cathode rays, so that there is a very large ionization." He 
concludes, finally, " that the very large secondary radiations which 
some substances appear to give, therefore owe their magnitude 
largely to the fact that the air in which they are measured is 
sometimes ten to twenty times as favourable to them as to the 
primary rays which produced them." 

I was, of course, not unaware of the increased ionizing power 
of the softer rays from ethyl bromide as compared with those 
from air, and in my original paper, I endeavoured to correct for 
this fact, on what seemed to be, in the absence of direct evidence, 
the reasonable assumption that the ionization produced in air by 
rays of differing hardness, was proportional to the amount of 
absorption undergone by the rays in the secondary ionization 
chamber. The final values given in Column HI, Table 1, of my 
earlier paper are reduced on this assumption. With this correc- 
tion the relative intensity of ethyl bromide compared with air 
became 217, as given in the table. 

The assumption on which this calculation is made has never 

* Crowther, Phil. Mag. [6], Vol. xiv. p. 653, 1907. 

t Bragg and Glasson, Proc. Roy. Soc. Suzith Australia, Vol. xxxi. Oct. 1908, 

102 Mr Growther, On the secondary Rontgen radiation 

been directly verified, and in the light of Prof. Bragg's interesting 
suggestion, it was thought desirable to make some direct experi- 
ments on the point, and to compare the relative amounts of 
ionization produced by the secondary rays from ethyl bromide 
and from air, in some gas not so unfavourable as air, to the 
harder radiations. 

Methyl iodide, and ethyl bromide suggested themselves as the 
most likely for the experiments. The ionization produced by the 
primary rays in both is very large, and their coefficients of absorp- 
tion for the primary rays are also large. The values obtained for 
ethyl bromide, however, vary less rapidly with the nature of the 
rays than those for methyl iodide, so that comparable results 
are more easily obtainable with it than with the latter. On the 
whole, therefore, ethyl bromide was preferred; and the experiment 
consisted in comparing the amounts of ionization produced in 
ethyl bromide by the secondary rays from ethyl bromide, and 
from air. 

To Cells 



To Electrosfiope 


To EarlTi 

; / 




-r^ y= V- 

/ A 

The apparatus employed was a modification of that used in 
my previous researches* on the subject, and it will not be neces- 
sary to describe it in any great detail. The radiating gas was 
contained in a rectangular brass box A ; the primary rays entering 
through an aluminium window G ; while the secondary rays passed 

* Crowther, Phil. Mag. [6], Vol. xiv. p. 653, 1907. 

from air and ethyl bromide. 103 

upwards through a second aluminium window d into the secondary 
ionization chamber B. A portion of the primary rays passed out 
through a third aluminium window e, into an ionization chamber 
P where its intensity could be measured. 

The secondary ionization chamber B was of a different form to 
that employed in the previous experiments. It is very difficult 
to obtain the " saturation current " across a cylindrical ionization 
chamber, with a central wire electrode, such as was previously 
employed. An elementary calculation will shew that the field 
near the outer cylinder is only a small fraction of the average 
intensity between the electrodes, and so, to obtain saturation in 
this part of the gas it is necessary to apply a potential between 
the electrodes much greater than would be required in the case 
of a uniform field. As ethyl bromide is a somewhat difficult gas 
to saturate, the cylindrical form of ionization chamber was 
abandoned in favour of the form shewn in the figure. The 
central electrode is here a thin sheet of aluminium leaf stretched 
on a circular frame of copper wire. It is insulated by a quartz 
tube passing through an earthed guard ring ; the latter in turn, 
being insulated from the case (which is charged to a potential of 
480 volts) by an ebonite stopper. The ends f, f of the chamber 
are of aluminium foil which is held in position by a similar device 
to that employed for the windows in the box A, and described in 
a previous paper. The various joints are made air-tight by means 
of sealing wax. 

The chamber B is so placed with respect to A, that no secondary 
radiation from the walls of the latter can enter it. The currents 
through the two chambers B and P are measured by Wilson elec- 
troscopes in the usual way. 

The ionization chamber B is filled with ethyl bromide vapour 
at some suitable known pressure (about 200 mm. of mercury). 
The ratio of the currents through B and P is then measured with 
the box A filled first with air and then with ethyl bromide vapour 
at a known pressure. From the ratio of these two quantities we 
can find the relative amounts of ionization produced in the ioniza- 
tion chamber B by the secondary rays from air and ethyl bromide. 
Corrections have to be applied for the absorption of the secondary 
rays from the gas by the aluminium windows d and/"; and in the 
case of ethyl bromide, for the absorption of the primary and 
secondary rays in the gas of the gas chamber A. Finally we have 
to correct for the fact that the air and ethyl bromide are employed 
at different pressures. The various data required are known, and 
have been given in a previous paper on the passage of Rontgen 
rays through gases*, and the various corrections required can be 
easily performed. In this way it was found that the amounts of 
* Proc. Roy. Soc. Vol. lxxxii. p. 103 (1909). 

VOL. XV. PT. II. 8 

104 Mr Growther, On the secondary Rontgen radiation 

ionization produced in ethyl bromide by the secondary rays from 
ethyl bromide was 162 times that produced in ethyl bromide by 
the secondary rays from air under similar conditions. The corre- 
sponding value when air was used in the secondary ionization 
chamber was 543. It will thus be at once apparent that the 
ethyl bromide is much more favourable to the secondary rays from 
air than is air itself. 

But although the coefficients of absorption for different types 
of rays are more nearly equal for ethyl bromide than for air, they 
are still not independent of the hardness of the rays. The coeffi- 
cient of absorption of ethyl bromide for the primary rays used in 
these experiments, and therefore, also, for the secondary rays from 
air, was 'IS ; while its coefficient of absorption for its own secondary 
rays was "SS. Knowing the dimensions of the secondary ionization 
chamber B, and the pressure of the ethyl bromide in it, we can 
easily calculate the quantity of each type of ray absorbed by the 
gas in B. The width of the chamber was 3'5 cms. ; the pressure 
of the ethyl bromide in it 210 mm. of mercury. The percentage 
energy absorbed in the gas was, therefore, for the soft rays from 
ethyl bromide 19'2 °/^, and for the hard rays from air 12"4 %. If 
we assume that the amount of ionization produced is proportional 
to the amount of energy absorbed, we thus obtain for the relative 
amount of secondary radiation from ethyl bromide, compared 
with that from air, the final value 105 ; a result which is just 
about half that given in the original paper. Though thus con- 
siderably reduced, the secondary radiation from ethyl bromide 
still remains abnormally large. If we divide the relative secondary 
radiation by the relative density (o"78) we obtain the value 28 ; 
as against TO for the lighter elements; 8"0 for stannic chloride; 
and 8'4 for methyl iodide. 

It may be noted that, as the penetrating power of the 
secondary rays from stannic chloride, methyl iodide, and sub- 
stances of low atomic weight is the same as that of the secondary 
rays from air, the values obtained for the relative amounts of 
secondary radiation from these substances compared with air are 
not subject to any correction for selective absorption by the 
medium in the secondary ionization chamber, and therefore need 
no modification as the result of the present experiments. 

It has already been mentioned that in my original paper the 
relative ionizations produced in the air of the secondary ionization 
chamber by the different types of secondary rays were corrected 
on the assumption that the amount of ionization was proportional 
to the absorption. It was not possible, however, to measure the 
absorption of the different types of rays in air itself, the absorption 
by air being too small to be readily appreciable. What was done, 
therefore, was to measure the absorption of the rays by some 

frow, air and ethyl bromide. 105 

solid, and to assume that the ratio of the absorptions was the same 
for solid and gas. The phenomena of the selective transmission 
of the primary rays by air, which Bragg has pointed out in the 
paper already quoted, were at the time far from clear, and unfor- 
tunately tinfoil, a substance which does not shew this selective 
transmission of hard rays, was employed as the absorbing substance, 
and the values obtained for it were used in calculating the final 
result. The ratio of the coefficients of absorption of the secondary 
rays from ethyl bromide, and air, is for tinfoil approximately 2"8. 
The ratio for air itself is undoubtedly much higher. As mentioned 
above it is hardly possible to measure the absorption of air itself 
for these different rays, the absorption in any reasonable distance 
being so small ; but filter paper suggests itself as being composed 
of elements approximating very nearly in atomic weight to air. 
The absorption of filter paper, therefore, has been measured for 
the secondary rays from ethyl bromide and air ; and the ratio of 
the two coefficients of absorption for filter paper has been found to 
be 5"4. Using this corrected value for the coefficients of absorp- 
tion, and assuming again that the ionization is proportional to the 
energy absorbed (that is to say in the case of air, where the 
percentage absorbed is very small, to the coefficients of absorption), 
we deduce from our original measurements of secondary radiation 
made in air the corrected value 101, for the relative amount of 
secondary radiation from ethyl bromide. This value agrees re- 
markably well with the value 105 obtained for the same quantity 
from the present measurements, using ethyl bromide as the 
absorbing gas in the secondary ionization chamber. 


The relative amounts of ionization produced in ethyl bromide 
vapour by the secondary Rontgen radiation from ethyl bromide 
and air have been measured. From this, knowing the absorption 
of ethyl bromide for the two kinds of secondary rays, the relative 
intensity of the secondary radiation from ethyl bromide has been 
calculated ; and has been found to be 105 times that from air. 

The relative absorption of the two kinds of secondary rays has 
been measured for a substance of low atomic weight ; and the 
value obtained has been used to correct the original results for the 
secondary radiation from ethyl bromide, which were obtained from 
measurements made in air. With this correction, the two values 
for the secondary radiation from ethyl bromide, obtained by 
measurements made in ethyl bromide, and in air, have been 
shewn to be in agreement. 

In conclusion I wish to express my best thanks to Prof. Sir J. J. 
Thomson for his kindly interest in these experiments. 


106 Mr Laby, A string electrometer. 

A string electrometer. By T. H. Laby, B.A., Research Student, 
Emmanuel College, Cambridge, Joule Student of the Royal 

[Read 25 January 1909.] 

The minute force, 10~^ dynes, that is sufficient to perceptibly 
deflect a stretched silvered quartz fibre, is of the same order of 
smallness as that acting on the gold leaf of the most sensitive of 
the usual electroscopes. This suggested that the fragile and irregu- 
larly shaped gold leaf might be replaced with advantage by a 
silvered quartz fibre. 

I constructed a very simple form of string electrometer, and 
was testing it, when through Mr N. R. Campbell I learnt that 
Dr C. V. Burton had designed a model of a similar instrument. 
The Cambridge Scientific Instrument Company kindly lent me it 
to test. The results given below were obtained with this instru- 
ment, after it had been somewhat altered. 

The Einthoven Galvanometer. 

Einthoven has found that the movements of a stretched quartz 
fibre subject to a varying lateral force afford a precise and delicate 
means of measuring that stress. With his string galvanometer, in 
which a silvered fibre replaces the usual suspended coil, he has 
obtained photographs of the moving fibre on a falling plate using 
a magnification of about 500. Even with this magnification the 
motion of the fibre was so free from irregularities of an extraneous 
origin that Einthoven has been able to subject the oscillograph 
curves thus obtained to a minute analysis*. He has also followed 
vibrations with a frequency of 3000 per sec. The lightness 
(from 6 X 10~^ to 5 x 10"'' gm. per cm.) and excellent elastic 
properties of the silvered quartz make such results possible. 

Description of the Instrument. 

The string electrometer (see fig. 1) used in these experiments 
consisted of two vertical insulated plates, A, B, 15 cm. long by 
•8 cm. thick with their edges parallel and at an adjustable distance 

* Kon. Ak. van Weten, te Amsterdam, viii. p. 210, 1906. 

Mr Lahy, A slicing electrometer. 


These plates were connected to the ends of a battery, CD, the 
middle of which was earthed. The silvered quartz fibre, EF, 
is stretched parallel to and equidistant from the two plates A, B; 
this position of the string relative to A and B is attained by the 
lateral movement of its points of support, E, F; while its tension, 
which has to be kept very constant, is controlled by the screw S. 

Fig. 1. 

The terminals of the middle cell M, of the battery G, D, were 
connected to the potentiometer Rr, the middle of which was 
earthed, while the connection to the fibre could be moved from R 
to r, i.e. its potential varied from —1 volt to 1 volt by steps of 1/50 
of a volt. 

As the fibre was not highly insulated, tests could not be made 
with it isolated, so that the results given later, it should be pointed 
out, were got with the potential of the fibre maintained. 

The motion of the middle of the fibre was observed by means 
of a microscope with a Zeiss achromatic objective A, and micro- 
meter eye-piece No. 3. The tube length was such as to give 
a magnification of 100. A slight illumination gave a sharp image 
of the black silvered fibre on a bright ground. 


Mr Laby, A string electrometer. 

Properties of a String Electrometer. 

The purpose of the tests was to find how : 

(1) the sensitiveness, 

(2) the oscillograph powers of the electrometer depended on 

(a) distance of the plates apart, 
(6) their potential difference, 
(c) the tension on the fibre. 

Potential difference between plates in volts 
Fig. 2. 

Plates far apart (1"1 cm.). The plates were set far apart 
(compared to the distance moved through by the fibre) and then 

M7' Lahy, A string electrometer. 


the sensitiveness (deflection per volt) was observed for a range of 
plate potential differences. With a new tension the same observa- 
tions were repeated. In this way the equal tension potential 
difference-sensitiveness curves (figs. 2 and 3) were obtained. The 

S- '0 

Potential difference between plates in volts 
Fig. 3. 

sensitiveness is expressed in eye-piece divisions per volt on the 
fibre: one eye-piece division =-0012 cm. movement of the fibre 
itself. These curves express many of the properties of the instru- 
ment. We see from them that a high sensitiveness was obtained 
with the fibre not very tight (curves 1, 2, figs. 2 and 3), which in- 
creased with the P.D. between the plates to its greatest value in fig. 3 
for 18 volts, when the sensitiveness was 60. There is a practical 


Mr Lahy, A string electrometet. 

limit, as will be explained later, to the sensitiveness that may be 
obtained by increasing the potential difference, or decreasing the 
tension. With the plates at this distance apart the position of 
the fibre was plotted against its voltage and the curve of fig. 4 
obtained. It will be observed that one of these graphs is a 
straight line, so that the deflection is proportional to the voltage 
even for high sensitiveness, and for a wide range (for an electro- 
scope) of voltages. 

50 r 

•2 -4 -6 

Potential of fibre in volts 




Fig. 4. 

Plates near together {<6'Q mm. and 3'3 mm.). When the dis- 
tance between the plates was reduced to 6'6 mm. and finally 
to 3'3 mm. several properties of the instrument, to be seen in 
figs. 3 and 5, came into greater evidence. 

The chief change in the potential difference-sensitiveness 
curves (fig. 3, plates at 6'67 mm.) is that smaller p.d.'s appear to 

Mr Lahy, A string electrometer. 


give a larger sensitiveness for a given tension, or as is to be expected 
theoretically the sensitiveness for a given fibre tension depends 
on Vjd?, where V is the P.D. and d the distance between the plates. 
This could not be fully proved as the tension of the fibre did not 
remain sufficiently constant. With the plates at 3"3 mm. apart 
the deflection of the fibre as its potential changed became markedly 
different. With the fibre tight its deflection was still proportional 
to its potential (the straight line of fig. 5), but when slackened the 

•15 -1 -05 

Potential of fibre in volts 

Fig. 5. 

position, which the fibre took up for different potentials, is repre- 
sented by the curve AB (fig. 5); on lowering the tension still 
further the fibre had two stable positions and apparently an 
unstable one not experimentally realisable. In other words, if the 
fibre is slackened the sensitiveness increases, but for a decreasing 
range of voltages : theoretically we pass through infinite sensitive- 
ness to instability. This property of the instrument, which sets 
a superior limit to its useful sensitiveness, is best grasped by 
examining fig. 5. 

In Mr C. T. R. Wilson's* tilted electroscope, as is well known, 
this property is used to obtain a high sensitiveness, the adjust- 
ments (plate potential, tilt and length of gold leaf) are altered 

* Proc. Camb. Phil. Soc. xii. p. 135, 1903. 

112 Mr Laby, A string electrometer. 

till the portion AB (fig. 5) of the deflection potential curve is 

Characteristics of the String Electroscope. 

The fibre will stand vibration and sudden large changes of 
voltage without breaking. The instrument has been carried on a 
bicycle without damage to the fibre. 

Sensitiveness. No common standard of comparison has yet been 
proposed for electroscopes. The unit of deflection used in this 
paper is one division of the micrometer eye-piece : 1/5 of this 
could be read with certainty. The closeness with which the 
observations fall on curves shews that the unit chosen is not 
unduly small. In fig. 4 (plates 6'6 mm. apart) a sensitiveness 
of 50 divisions per volt is shewn. At the same time the curve 
is nearly a straight line, i.e. the deflection is approximately pro- 
portional to the voltage, and the p.d. between the plates was less 
than 40 volts. The electrometer has been quite sensitive using 
only 20 volts p.d. ; such a small p.d. could be kept constant more 
readily (by the use of Weston cells, say) than the larger ones 
usually required for electroscopes and electrometers. On the 
other hand, large voltages, which require to be constant, would 
generally still be required, for example, to saturate an ionised gas. 
With the plates at 3'3 mm. apart and a p.d. of 36 volts a sensi- 
tiveness of 100 divisions per volt over a range of "4 volt was 
readily obtained. 

Oscillograph Uses. 

I do not think, however, that the value of the string electro- 
meter will lie especially in its sensitiveness. It is not difficult to 
make a gold leaf electroscope highly sensitive over a small range. 
But there is a distinct need now for an electrometer capable of 
automatically recording rapid changes of voltage, in the study 
of discontinuous phenomena in the direction indicated by von 
Schweidler*. For example in the beautiful experiment of 
Rutherford and Geiger of counting the number of a particles, 
which arrive in an ionisation vessel, by the excursions of an elec- 
trometer the smaller the free period of the electrometer the 

To test the oscillograph powers of the instrument, the plates 
were placed 3 mm. apart at a P.D. of 120 volts, and the tension 

* Congres international poxir I'etude de la radiologie et de I'ionisation, Liege, 

Mr Lahy, A sti^ing electrometer. 113 

on the fibre increased ; the sensitiveness was then 50 divisions per 
volt. Yet the motion of the fibre was dead beat, and it took up a 
new position in less than one-tenth of a second. Since the move- 
ments of a fibre can be readily recorded photographically the 
instrument seems to promise well as an oscillograph. Further 
experiments are being made on this use of it. 

It should be recalled that all the above experiments were 
made with a steady source of potential. Mr H. Darwin has de- 
signed a new instrument in the light of the experience obtained 
with this one ; when it is finished more complete tests than these 
will be made with it. 

I am indebted to Mr Horace Darwin and Mr Whipple for 
having lent me the string electrometer I used, and for having had 
certain alterations made in it. I am grateful to Prof. Sir J. J. 
Thomson for the encouraging interest he took in these experi- 

114 Mr Taylor, Interference fy^wges ivith feeble light. 

Interference fringes with feeble light. By G. I. Taylor, B.A., 
Trinity College. (Communicated by Professor Sir J. J. Thomson, 

[Bead 25 January 1909.] 

The phenomena of ionisation by light and by Rontgen rays 
have led to a theory according to which energy is distributed 
unevenly over the wave-front (J. J. Thomson, Proc. Camb. Phil. 
Soc. XIV. p. 417, 1907). There are regions of maximum energy 
widely separated by large undisturbed areas. When the intensity 
of light is reduced these regions become more widely separated, 
but the amount of energy in any one of them does not change ; 
that is, they are indivisible units. 

So far all the evidence brought forward in support of the 
theory has been of an indirect nature ; for all ordinary optical 
phenomena are average effects, and are therefore incapable of 
differentiating between the usual electromagnetic theory and the 
modification of it that we are considering. Sir J. J. Thomson 
however suggested that if the intensity of light in a diffraction 
pattern were so greatly reduced that only a few of these indivisible 
units of energy should occur on a Huygens zone at once the ordinary 
phenomena of diffraction would be modified. Photographs were 
taken of the shadow of a needle, the source of light being a 
narrow slit placed in front of a gas flame. The intensity of the 
light was reduced by means of smoked glass screens. 

Before making any exposures it was necessary to find out what 
proportion of the light was cut off by these screens. A plate was 
exposed to direct gas light for a certain time. The gas flame was 
then shaded by the various screens that were to be used, and other 
plates of the same kind were exposed till they came out as black 
as the first plate on being completely developed. The times of 
exposure necessary to produce this result were taken as inversely 
proportional to the intensities. Experiments made to test the 
truth of this assumption shewed it to be true if the light was 
not very feeble. 

Five diffraction photographs were then taken, the first with 
direct light and the others with the various screens inserted 
between the gas flame and the slit. The time of exposure for the 
first photograph was obtained by trial, a certain standard of 
blackness being attained by the plate when fully developed. The 

Mr Taylor, Interference fringes with feeble light. 115 

remaining times of exposure were taken from the first in the 
inverse ratio of the corresponding intensities. The longest time 
was 2000 hours or about 3 months. In no case was there any 
diminution in the sharpness of the pattern although the plates did 
not all reach the standard blackness of the first photograph. 

In order to get some idea of the energy of the light falling on 
the plates in these experiments a plate of the same kind was 
exposed at a distance of two metres from a standard candle till 
complete development brought it up to the standard of blackness. 
Ten seconds sufficed for this. A simple calculation will shew that 
the amount of energy falling on the plate during the longest 
exposure was the same as that due to a standard candle burning 
at a distance slightly exceeding a mile. Taking the value given 
by.Drude for the energy in the visible part of the spectrum of a 
standard candle, the amount of energy falling on 1 square centi- 
metre of the plate is 5 x 10"" ergs per sec. and the amount of 
energy per cubic centimetre of this radiation is 1*6 x 10~^^ ergs. 

According to Sir J. J. Thomson this value sets an upper 
limit to the amount of energy contained in one of the indivisible 
units mentioned above. 

116 Mr Richmond, On the parametric representation, etc. 

On the parametric representation of the coordinates of points 
on a cubic surface in space of four dimensions. By H. W. 
Richmond, M.A., King's College. 

[Received and read 8 March 1909.] 

By a cubic surface in space of four dimensions is here under- 
stood the locus represented by a homogeneous equation of the 
third degree in five variables, and the problem considered is a 
method of expressing the ratios of the five variables as algebraic 
functions of three parameters. Should the cubic surface possess a 
double point, projection with that point as vertex leads at once to 
a solution. 

If however the surface has no double point, take any straight 
line L which lies wholly on the surface ; six such lines pass through 
each point and twenty-seven lie in every space of three dimensions, 
at least three of the latter being real. Through L and any point 
P of the surface can be drawn an *S^2. whose intersection with the 
surface will consist of the Hue L and a conic, which must intersect 
L in two points, Qi and Qg- Conversely, if any two points Qi and 
Q2 be chosen upon L, the tangent S-^s at Qi and Q.2 have in common 
an S^ which contains L and a conic passing through Qi ^'^d Q^. 
Thus if points of the line L are determined by a parameter, 0, 
then to any two values of it <^i and <^2 correspond two points Q^ 
and Q^, and consequently a conic passing through Q^ and Q>^. 
Another parameter -»|r will define each point of the conic, and thus 
the coordinates of each point of the surface will be algebraic 
functions of <^i, <^2 and ■^. 

In fact the equation 

u"x + 2uvy + v^z 4- 2wX, -f- 2vyu, -\-p = (1), 

in which X and yu, are quadratic functions and p a cubic function 
of X, y, z, represents a quite general cubic surface on which the 
line L, cc= y = z= lies. A point on L is determined by a 
parameter ^ if v — u .(f); and the tangent Ss at the point is 

X + 2y^ + z(f)^ = 0. 

Thus on the S2 common to the tangent S-Js at points where ^ 
has the values (f)i and (j).2, 

X -.y : z :: (fy^cf).^ : - -^ ((/)i + (f)^) : 1 ; 

and if in (1) we substitute x = z . (f)i<f).2, y = — \z {(f>i + (po) and then 
write M01 — v = z.-^, the problem is solved. 

Mr Campbell, The study of discontinuous phenomena. 117 

The study of discontinuous phenomena. By Norman 
Campbell, M.A., Fellow of Trinity College, Cambridge. 

[Bead 22 February 1909.] 

§ 1. The application by Kohlrausch* by Meyer and Regenerf 
and by GeigerJ of von Schweidler's theory§ of the discontinuities 
in the emission of rays by a radioactive substance to the measure- 
ment of the charge carried by an a particle opens up a new and 
most important field of physical research. The ingenuity of the 
method must always give great interest to their work, but it has 
lost much of its immediate importance since Rutherford and Geiger|| 
have measured the same quantity by the more direct and probably 
essentially more accurate method of counting the number of particles, 
one at a time. The justification of the lengthy discussion of von 
Schweidler's method which is given in the following pages is two- 
fold. In the first place, it is believed that the discussion by the 
four authors first named of the principles according to which their 
observations should be interpreted is neither exhaustive nor com- 
pletely devoid of error, and that a more thorough discussion will 
enable the results obtained by von Schweidler's theory to rival in 
accuracy those attained by Rutherford and Geiger. In the second 
place, it should be remembered that radioactivity is not the only 
discontinuous process which we study. The trend of modern theory 
is everywhere to replace by discontinuity the continuity which was 
the basis of the science of the last century. Any method which is 
especially applicable to discontinuous processes is certain to be 
fruitful of results in every department of investigation, and any 
considerations which can be advanced in the elucidation of such 
a method are not devoid of value ; at the present time I am 
engaged in an attempt to apply the method to a totally different 
form of ionisation current. 

I 2. It will be desirable first to put von Schweidler's theory 
in a slightly more general and a somewhat more accurate form. 
The author of that theory used in his calculations Bernoulli's 
integral of probability. Now the use of the integral calculus in 
this case is open to the objection that it assumes that the number 
of possible cases, the probability of which is considered, is so large 
that it may be regarded as infinite. But the essential feature 

* Wien. Ber. 1906, p. 673. + An. d. Phys. xxv. p. 757. 

+ Phil. Mag. April, 1908, p. 539. § See Kohlrausch, loc. cit. 

II Proc. Roy. Soc. A. 81, p. 191. 

118 Mr Campbell, The study of discontinuous phenomena. 

of the phenomena that we propose to investigate is that they are 
discontinuous, that is to say, that they are to be regarded as made 
up of a finite number of events and not of an infinite number: in 
some eases to which we may have to apply our theory it is by no 
means certain tliat the number is even very hxrge. By using the 
integral calculus we assume in our mathematical considerations 
the proposition which we deny in our physical considerations. 
Accordingly we must confine ourselves throughout to finite 

Consider a series of s trials in each of which one of the 
two mutually exclusive events A and B must happen. Let the 
probability that A happens be p and the probability that B 
happens be q. Then it can be shown easily that if A happens 
m times and B m — s times, the most probable value of in is ps: 
and further that the probability that A happens ps — x times is 



ps-x f^qs+X 

{ps-:v)l{qs + :vy. 

We shall require the mean value of the 'deviation' w for 
a very large number (<r) of sets of s trials. There are three 
chief forms of mean value, ;r, x, and \x\. Remembering the 

c{p + qy-^ .q = S nA„p'-" q" 


and c{c — l){p + qY~'^ q- + c (p + qY'^ 5* = ^ n'Anp°~"' q'\ 


where A,. = -, V-; — . 

" (c - n) \n\ 

we can easily show that, since p + q = 1, 

— •^■^" «* s ' 

^^= Sa-^ ^ -— pps-xqqs+x 

x=ps (ps - iv) ! {qs + X) ! ^ 
= spq 

and that \x\ = a / -^ , if s is large *. 

The mean values a"^ and x are the same as those given by 
von Schweidler for the case when 5 is very large: but we see that 
their form is quite independent of any assumptions as to the order 
of magnitude of s, p, q. But the form of \x\ is not so independent, 
and no further use will be made of this mean. 

* See Bertrand, Calcul des probabilites, chap. iv. 

Mr Campbell, The study of discontinuous phenomena. 119 

In calculating these means we have assumed that a ' very 
large number' of sets of s trials are taken. It is desirable to 
inquire how large the number must be in order to reduce the 
probable error within any desired limits. The problem is very 
similar to that of determining the probable error of the calculated 
probable error of a set of observations. If s is very large, it is 
well known that the expression given for the probability of a 
'deviation' x may be reduced by Stirling's theorem to an exponential 
form, so that the probability that the value of x lies between x-^ 
and x^ + dx is 

Q-K^xi^ ^g/,^ where h = 

s/ir ' '^2pqs 

Accordingly the probability of a given set of o- values of x, Xi, x^, 
X3... such that Xi' -\- x^ + x^ + ... xj^ = ara^ is 

h X"' 

~i- dx] e-'^'-<^»'. 

Vtt / 

We shall find that our observations give us the value of 
aa^ = liX^. h is then chosen so as to make the probability of the 
occurrence of this value of X^c^ a maximum : we find 

h"^ = TTFT— or a:;2 = — - = spq, as before. 
zzx^ 2h 

Accepting these values, we can find the probability that h has 
the value h + uh: this probability is 

\ Vtt / 

f h \'"' 
where G = (-^ dxj e-^'-''"'\ 

Hence the ' measure of precision ' of A is \/n. In order that the 
probable error may be less than 1 °/^, \/n must be greater than 
100 or n greater than 10^ In order to attain this degree of 
accuracy we must take 10* sets of the series of s trials. We have 
assumed that s is large, but since the expression for the probability 
will be of nearly the same form whatever the value of s and since 
we require only a rough value for the measure of precision, we 
may apply the result to all values of s such as are likely to occur. 

I 3. Let us now apply this theorem to such cases as are likely 
to occur in physical investigation. Suppose that a very large 
number of events NT happen in a time T. If we fix our attention 
on a period t within T and small compared to it, the chance that 

any one of these events will happen within t is „: it must be noted 

VOL, XV, PT, II, 9 

120 Mr Gam'phell, The study of discontinuous phenomena. 

that the probability is the same whether the parts of t are adjacent, 
so that T is continuous, or whether they are scattered at random. 

Now the occurrence of the NT events correspond to the 
s trials, and the events A and B correspond to the falling of one 
of the NT events respectively within or without r. Hence 

NT = s, p = ^, g = l-J. 

Then if observations are taken over <t periods, each of length T, 
and if Nt + Xi, Nt -\- X2, . . . Nt + 00^ are the number of the events 
which happen within the period r is the 1st, 2nd, ... o-th observa- 
tions, we have proved that 

^^ = NT.^.{l-^^ 

If we make t small compared to T, we have 

'^ = Nt (1). 

In the particular case of radioactivity, T is the time over 
which the activity of the substance suffers no appreciable decay : 
the NT events are the breaking up of NT atoms. If, then, we 
had some instrument which would indicate the number of atoms 
which break up during any period r short compared to T, we 
might discover the value of N by taking a sufficient number of 
observations and equating to Nr the sums of the squares of their 
deviations from the means or ' fluctuations.' An electrometer 
connected to an ionisation vessel which could be exposed for a 
known time to the action of the rays from the substance would be 
such an instrument. But it must be noted that, though the 

absolute value of the mean * fluctuation ' Jx^ = \/Nt can be made 
as large as we please by increasing the period t, the ratio of that 
value to the value of the whole number of rays emitted during 

the period t is equal to „ and decreases with an increase of r. 

Numerical calculation shows that (unless Rutherford and Geiger's 
method of magnifying the effect due to a single ray is employed) 
no value for t can be found for which the mean fluctuation exceeds 
the probable error in the measurement of the value of the total 

Accordingly all who have attempted to apply von Schweidler's 
theory have employed some balancing method by which the mean 
total current is reduced to zero, so that the fluctuations become 
fluctuations about the zero and only their absolute magnitude 
need be taken into account. These may be made as large as is 
desired by an increase in N and r. Geiger and, before him. 

Mr Campbell, The study of discontinuous phenomena. 121 

Kohlrausch, balanced against each other currents due to two 
independent radioactive sources. Since some doubt has been 
thrown on Kohlrausch's results by later workers no further reference 
will be made to them. Meyer and Regener balanced the current 
from one radioactive source by means of a Bronson resistance, to 
the terminals of which a compensating potential difference was 
applied by a potentiometer arrangement. And these two arrange- 
ments are examples of the only two principles which seem possible 
in any measurements of this kind. 

But it must be noted that, if a reading of the instrument 
is taken while the rays are acting, this reading will not indicate 
the value of the fluctuation at the moment of observation. The 
instrument has inertia, and its indication at any time is a function 
of the fluctuations during some finite period preceding the moment 
of observation. In Geiger's method it might be possible to get rid 
of the inertia of the needle by removing the sources of rays after 
a definite period of action and allowing the instrument to take 
up a steady position before the reading is taken. But we shall 
see that there are grave practical difficulties in such a procedure : 
and the method is not applicable to Meyer and Regener's ob- 
servations by reason of the ' inertia ' of the Bronson resistance. 
Accordingly the problem before us is to determine the relation 
between the observed fluctuations, which depend on the constants 
of the instrument, and the real fluctuations which depend only 
on the nature of the source. We will consider first the method 
of Meyer and Regener. 

Meyer and Regener s method. 

I 4. Let a charge E be given to the electrode system when 
the electrometer is at zero and at rest. If the capacity of the 
electrode system be G, the resulting potential will be EjC. If 
the current through" the Bronson resistance is proportional to the 
potential difference between its terminals, this potential difference 
will diminish exponentially with the time, so that the potential 
difference acting on the electrometer needle at a time t after the 
charge has been communicated is 


where p is a constant depending only on the nature of the 

Let / be the moment of inertia of the needle, [x the coefficient 
of damping, k the coefficient of torsion and KV the couple acting 
on the needle when the p.d. between the quadrants is V. (It is 
assumed that the deflection 6 is proportional to the steady p.d. 


122 Mr Campbell, The study of discontinuous phenomena. 

applied.) Then the equation of motion of the needle subsequent 
to the communication of a charge E is 

I^ + l^f^+ke-K.EIC.e-P^ = (2). 

Taking into account the initial conditions the solution is : . 

^ Ae-'^' + Be-P' + Pe-i" (3), 


_ /x-\V-4//> - KE ^p^-P 

"" 21 ' C{If-fip + k)' a-yS' 

^~ 21 ' a-^' 

All these quantities can be found by suitable experiments 
on the electrometer and the resistance. Accurate determinations 
of them would require some ingenuity and labour, but they can 
be found with accurac}^ sufficient for the purpose of this research 
by methods which will be obvious to everyone. (See § 10.) 

It is easy to show that, subject to the assumptions njade, the 
effects of charges communicated at any times, Tj, T3, ... T;„, are the 
same as if the needle had been at zero and at rest at the moments 
of communication. Hence the deflection at a time T, which is 
subsequent to the communication of all the m charges, will be 
given by 

&T=K^Jl (^^"'"'^""••' + 5e-^(2^-^'-t +Pe-i'(r-v)) (4)_ 

Let us now change the origin of time to the time T, which 
is the time of observation. Writing 1,.' for the time before the 
moment of observation at which the rth particle was emitted, 
we have 

Ot - ^721 {Ae-'^'r + Be-^'' + Pe-^"0 (5) 

= KV:f{tr){^^j) (6). 

6t is a function both of the number of particles emitted and 
the times at which they were emitted. In the case which w^e are 
considering we do not know these times and hence cannot determine 
the number directly from a single observation. But I shall proceed 
to show that we can determine it from the average of a large 
number of observed values of ^V- (It will appear later why we 
have to take the average of 6'^x find not of l^r|.) For the main 
principle of the argument I am indebted to Mr G. H. Hardy, 
Fellow and Mathematical Lecturer of Trinity College, Cambridge, 
who points out that though no elaborate analysis is necessary for 

Mr Campbell, The study of discontinuous phenomena. 123 

the solution of the problem, interesting questions are raised in a 
branch of mathematics which has received little attention. 

§ 5. Let the period of observation be divided up into m periods 


T = —, such that/(^/) may be considered sensibly constant during 

any one period t. The total length of the period of observation T 
(that is the time from the moment of insulating the electrode to 
that of taking the observation) will be considered to be the same 
for all observations : but from the form of /"(i/) it is clear that all 
periods T may be considered equal so long as aT, ^T and pT are 
all large compared with unity. 

Let yr be the number of particles emitted during the rth 
period t. Then, during any one period of observation, yr is a 
function of r. In this statement the word ' function ' is used in 
the widest possible sense, and not in the restricted sense often 
employed in analysis. Further, to each value of r during any one 
period T, corresponds one and only one value of y,.. Let us write 

2/.=</>w (n 

The function <^(r) has different forms in different periods T. 
Let there be v periods of observation and let the form of 4>(r) 
in the pth period be cf)p (r). Since (j) (r) can have a large number 
of forms, a definite meaning can be attached to the expression 
' the probability that ^ (r) has the form (f)p (r) ' : let ^p be this 

Let Nt + fl^i, Nt + X2, ... Nt + Xn be all the possible values of 
y : then (f)p (r) has m of these values during the m periods into 
which T is divided. The probability of the occurrence of any 
value Xr is, by § 2, 

{Nt + X,) ! {NT -Nt- Xr) ! \T) \ T) 

Hence the probability that ^ (r) has a definite m of the possible 
values of y, that is, the probability that <^ (r) has a definite 
form, is 

%i-%2. •..%m = ^P (8). 

Now it is important to notice, for this is the essential step 
in the argument, that the value of $p is not affected by the order 
in time in which the definite values of x^ occur, ^p is the same 
if the values of x^ are the same : it is not altered if x^ = a^ when 
r = u and a^ when r = v, instead of a^ when r = u and a„ when 
r = v. That is to say, (pp is wholly independent of r. 

Now if (fi(r) has the form <}>p(r), the corresponding value of 
^V will be 

^v = [s;:r</'pW/0'T)p (9). 

124 Mr Campbell, The study of discontinuous phenomena. 

The probability of this value of ^V is ^p : hence the sum of the 
values of 6'^t for the v periods of observation is given by 

2.6V=^2J:;^,K:r0p(r)/(rT)P (10), 

where the first sign of summation denotes summation with respect 
to all the forms which (r) takes in the v periods. 

§ G. Now summation with respect to a large number of forms 
of a function is not a process of which the methods have been 
elaborated. The value of the right-hand side of (10) cannot be 
found by a direct method, but it can be found by means of the 
following artifice. 

Expanding the squared factor in brackets we obtain 


Since <l>p is independent of r and s, we may reverse the order 
of summation and write 

X. e-^T = V XIT KZi ^:=i ^p [N'r^f(rT)f{sr) 

+ Nt (wr + Xs)f {rT)f(sT) + XrxJirT)f{sr)'\ (12), 

where the inner summation denotes that we take the average 
of the terms in square brackets over all periods of observation 
before summing them for the periods into which a single period 
of observation is divided. Now Nt is a constant and, as has been 
emphasized already, the average value of Xy or Xg is independent 
of r or s. The value of Xr in any one period T depends on the 
Value of r, but the probability that it will have that value is 
independent of r. Hence the average value of {x^ + x^ or x^-Xg 
is independent of /(rr) /(sr) and we may take the latter factor 
outside the summation with respect to p. Further we may notice 
that the average value of Xj. or Xg is zero by § 2 : hence the average 
of {Xr + Xg) is zero and the average value of x^Xg is zero, except 
when r = s. (It must be remembered that we are not taking the 
average for different values of r and s, but the average for the 
same values in different periods, so that no ^^ is a member of Xx^.) 
Hence our equation finally reduces to 

2.^v= V [s;:r K=x NH^f{rT)f{sT) + ^TJ^fivT) m\ ^.^A 


But Sp^)^ ^pXy? is simply the average value of x.,? for all periods T, 
that is, the average of Xy- for a very large number {v) of cases 
which are perfectly independent. By equation (1) above, the 
value of this average is Nt and hence 

2. e^T = V ts;::r s::r iYv/(rT)/(.T) + s;:r Nt .p {vt)] . . .(14). 

Mr Campbell, The study of discontinuous phenomena. 125 

Since /(?'t) is a continuous function of r, we may, with certain 
reservations to be considered later, replace the summations by 
integrations. Putting t = dt we find 

-tre'T=d^T = N' r^dt f(t) [*~^dtf{t) + N\'' dtf'it)... (15), 
V J «=o J t = o J t=^0 

or, remembering that 


I 7. 6t is the deflection of the needle from its zero position, 
but it will be found more convenient to express (16) in terms of 
the deflections of the needle from its mean position 6j- If ^'t 
denote the deflection from this mean position 

6^T=[{eT) + o'TY • an 

or since X6't=0 

WT=(dTY+0''^T (18). 

But, by an argument precisely similar to that given above, it can 
be shown that 


-(M-f) (-)• 

-s^ „ (A' P P^ 1AB , 2BP , 2PA\ ,„., 

We have found a relation between the unknown N (the number 
of particles emitted per second) and the quantities 6''^t, -^i P, P, 
a, y8, p, which are known, except so far as the charge E is 
concerned. PJ may be eliminated by the device of Meyer and 
Regener, who, by the use of their compensation method, measured 

not ^'V but (=1 = A^ The formula applicable to their experi- 

ments is 

^2 ^ p2 2AB IBP 2PA 

., 1 2^'^2^'^2p'^ a + /3'^ ^+p\ + a 

" =^- MTfT^y '''^- 

\a /3 pi 

Since £^ is a factor of J., jB, and P, it disappears in the ratio 
on the right hand of (21). 

126 Mr Campbell, The study of discontinuous phenomena. 

In passing it may be noted that the argument cannot be 
applied to the determination of |^r|. For, in the place of the 
square of the expression in brackets in (10) we should have the 
modulus of that expression. The modulus cannot be expanded 
in powers of the variables concerned and, accordingly, the order 
of the summations cannot be reversed. But on this reversal hangs 
the whole argument. In any case it would be advisable to avoid 
making use of | ^r | > for we have seen in § 2 that its value can 
be found with accuracy only if Nr is very large. 

§ 8. Before proceeding to discuss in detail the application 
of this theory to experiment we must consider how far the 
assumptions that have been made are likely to be fulfilled in 
experimental conditions. 

(1) We have assumed that r is small compared with T. 
Since we have seen that the theory is true whatever the value 
of Nt, it is clear that this assumption will cause no difficulty. 
We have already, in replacing the summations of the last 
paragraph by integrals, made t infinitesimal in comparison with 
the time constants of the instrument. But T is the whole period 
over which the physical conditions are constant, and it is clear 
that the experiment will be arranged so that these are constant 
over a period long compared with the time of observation. 

(2) (1) is the only condition which is essential to the theory, 
but we have seen that in order to get a probable error less than 
1 °/q, we must take a very large number of observations. The 
quantity v corresponds to the cr of § 2 and hence, for this 
degree of accuracy must be not less than 10*. Now it is clear 
that 10* observations cannot be made by any process of looking 
at the instrument and writing the observation down on paper: 
on a favourable estimate the process would need a month's 
continuous observation, day and night. Accordingly we must 
start our discussion of what instruments are to be used with 
considering how this large number of observations is to be taken. 

§ 9. The obvious method of taking this large number of 
observations is to record photographically the fluctuations of the 
instrument and to deduce the value of 6'^t from the resulting 

1 r^ 

trace by finding the value of ™ I 6''^j'dt. It would not be hard 

to devise a mechanical integrator which would give the value of 

I y^dx for any irregular curve, and, if this instrument were sensitive, 

its indications would correspond to an average taken over a very 
large number of cases : in fact, if dx is the smallest interval over 
which the instrument can be expected to distinguish between 
different values of y, then an integration over a length x would 

Mr Oamphell, The study of discontinuous phenomena. 127 

be equivalent to -j- observations. But it might appear at first 

sight that this method was unjustifiable because all the periods 
T would not be independent. But the only dependence between 
them is expressed by 

K4:'"' '^P (^o) /(^«) = ^r=; <^Po+.„ {r)f(r) (22), 

a relation which affects in no way the argument that the probable 
value of <f)^(ro) is independent of Vq: it is independent of everything 
except Nt and, as was shown in § 3, Nr is independent of the 
way T is selected. Or, if that proof seems inconclusive, we may 
remember that the average value of d'^j> for successive independent 
periods T must be the same at whatever moment (distant by an 
amount greater than T from the moment of insulation) the first 
period is dated. The proposed method consists of nothing more 
than averaging the averages of the same number of independent 
periods starting from different moments. 

Again, it may be argued that this method adds nothing in 
accuracy since the same observations are used over and over 
again. It is quite true that the method does nothing to diminish 
errors due to faulty observations of ^'y^but it does diminish errors 
due to the application of a theory in which we have assumed 
z/ = 00 to experiments in which v is finite. 

We may note also that photography adds to the accuracy 
in the observation of the position of a moving object. The only 
objection to the method is that greater weight is assigned to 
observations in the middle of a series than to those at the ends, 
but this objection does not seem to be serious; if observations are 
really of equal weight no harm is done by attributing a greater 
weight to a selection taken at random. 

§ 10. Let us now consider the instruments which it will be 
desirable to use. 

Firstly, we must be able to determine their constants with 
accuracy. The determination will doubtless be carried out by 
raising the electrode system (including the resistance) to a known 
potential v and watching the return of the needle to zero. (See 
I 16, below.) The equation of motion of the needle in this 
experiment will be 

= A'e-'^' + B'e-^' + P'e-P^ (23), 

where a, ^, p are as before and 

p.^ KV ^^^_ P(^-p)-V^ 

{Ip"" - fip + k)' a - /3 


128 Mr CampheU, The study of discontinuous phenomena. 

If the quantities a, ^, p are all different, it will be no easy 
matter to find their separate values: the analysis of a curve into 
three component exponentials involves great labour and the result 
is not likely to attain a high degree of accuracy. But most 
electrometers and electroscopes are either just periodic or just 
aperiodic, and they can be adjusted to the boundary condition 
between these two states without great difficulty. But in this 
boundary state 

V/A^ _ 4,1k = and a = /8. 

Let us suppose, then, that /3 = a + 7, where 7 is small compared 
to a. Taking into account the values of the constants, A, B,A', B', 
our equations undergo the following simplifications. (23) becomes 

61 = ( F - P') e--^* + Fe-v^ - rytB'e-'^' (23'), 

f{t) (equation (6)) reduces to 

f(t) = P (e-i'* - e-«) - r^tBe-'^' (6'), 

and (21 ) becomes 

p./l .1 2 \ /7/3 7/3 ^ , 7^^- 

,, 1 ^ \2p'^2a a + p)'^ Via? {a + pfJ^ 4«^ , , 

From (6') and (21') it is evident that nearly equal values 
of p and a are to be avoided: for, if these two quantities are 
equal, the two equations contain only terms involving the small 
quantity 7, which is hard to determine. Accordingly we must 
make one of the two quantities p and a very large and the other 
very small. There are three reasons why a should be made large 
and p small. 

(1) A small value of p corresponds to a high value of the 
resistance of the Bronson cell. But the greater this resistance, 
the greater is the deflection of the indicating instrument for a 
given current passing through the cell. Since it is easier to 
measure variations of the same proportional amount in a quantity, 
when that quantity is large, than when it is small, it is desirable 
that the steady deflection of the indicator, corresponding to the 
mean current, should be as great as possible. 

(2) A large value of a makes the terms involving the 
unknown small quantity 7 negligible. Any slight deviation from 
the boundary state between periodicity and aperiodicity will be 

(3) If a is large the required constants can be determined 
more easily from the equation (23'). Since p and a. are very 
different, the value of the terms involving e~** can be found from 

Mr Campbell, The study of discontinuous phenomena. 129 

the beginning or end of the observed decay curve, and those 
involving e~** from the end or beginning, according as a is greater 
or less than p. If a is large, t will be small for the part of the 
curve over which a is determined, and the term in 7 will be of 
very little importance. 

All the considerations advanced indicate that a Bronson cell 
should be chosen with as high a resistance as possible, and an 
indicating instrument with as short a period as possible. It 
seems desirable, therefore, to employ a gold-leaf or quartz-fibre 
electroscope in place of a Dolezalek electrometer. The only 
objection to the use of such an instrument is that it will be 
somewhat difficult to determine with accuracy the value of its 

time-constant -, which will be of the order of one second. But 

it must be remembered that, if a is large compared to p, the terms 

in (21') involving the former quantity are small compared to those 

involving the latter. Moreover, if the movement of the instrument 

is recorded by photography, the value of this quantity may be 

found by a method similar to that employed for measuring the 

constants of an Einthoven string galvanometer. The use of a 

Dolezalek electrometer seems prohibited, since, if it is aperiodic, 

its time-constant will be so great that it will be difficult to make 

the Bronson resistance so large as to avoid an approximate equality 

between a and p. 

§ 11. This elaborate discussion of experimental methods will 
be worthless unless there is some reason for believing that the 
method is not affected by some inevitable source of inaccuracy. 
There seems no reason why the observations should not be taken 
with very considerable accuracy, and the theory that has been 
given is, so far as I can see, complete and trustworthy. Let us 
consider the sources of systematic error which cannot be eliminated 
by the most careful experimentalist. 

Firstly, there is the Bronson resistance: the current through 
this instrument is subject to fluctuations which are added to those 
due to the source observed. These fluctuations can be diminished 
by using 13 rays in place of a. rays, as the agent of ionisation in 
the resistance: for though a much larger number of /S particles 
will be required and the absolute error, measured in number of 
13 particles, will be increased, the number of ions produced by a 
/S particle is so much less than the number produced by an a 
particle that the absolute error, measured in current, is less. But, 
against the use of /3 particles there is the objection that they 
cannot, with any convenience, be absorbed completely in the air 
of the resistance and hence chance fluctuations may arise from 
changes of temperature, etc. But in any case, the error due to 
the resistance can be eliminated by calculating the value of the 

180 Mr Campbell, The study of discontinuous phenomena. 

mean fluctuations by means of an approximate value of the 
electronic charge. (It may be noted that it might be possible 
to use some other form of high resistance, but probably all 
conductivity is ultimately discontinuous and we know far more 
about the conductivity of a gas than about that of a solid or 

Secondly, there is a source of error in the fluctuations of other 
parts of the apparatus during the period of observation: the cells 
used for maintaining the potential are the most likely source of 
trouble on this account. Perhaps such errors might be estimated 
and eliminated by means of carefully devised 'blank' experiments. 

Meyer and Regener seem to suggest that an error may be 
introduced by the finitude of the time required for a charge 
received by the electrode system to attain a steady distribution 
on that system. But it can be shown readily by a little arithmetic 
that error from this source is negligible. The error could only 
enter by fluctuations of the electrometer due to the vibration of 
the charge about its final position. Now, if R is the resistance 
of the vibrating circuit (in ohms), L its self-inductance (in henries), 
G its capacity (in farads), the period of vibration of the charge is 



Now taking the values of R, L, G, v/hich will give the greatest 
possible value for the period, we may put R = l, G— 10~^ L = 10~" 
(rememberiog that the self-inductance in henries of a solenoid 
of 100 turns and 1 cm,^ area is lO"*^). Then the period is about 
10~^ seconds. Now in the experiments of Geiger and Meyer and 
Regener the number of a particles coming off per second was 
never greater than 10": hence the period of oscillation of the 
charge is small not only compared with that of the instrument, 
but also with the average interval between two charges. 

I 12. It may be desirable to comment upon the work of 
Meyer and Regener in the light of the considerations which 
have been advanced. 

Meyer and Regener did not make use of the actual theory 
which has been elaborated, but they made use of its principle. 
They assumed that A^ was proportional to IjN and that the 
factor of proportionality depended on the instrumental constants 
only: this assumption, as we have seen, is justified. Accordingly 
they were justified in their expectation that, if the same instru- 
mental arrangements are used throughout, A^ should be pro- 
portional to IjN for diiferent values of N. Since they only took 
some 100 observations of A^ they could only hope for an agreement 

Mr Campbell, The study of discontinuous phenomena. 131 

between theory and experiment of about 10°/^, in place of the 
1 °/^ at which w^e have aimed. 

The best series of their results shows such an agreement 
as might have been anticipated, but in other series the value 
of A^ for large values of N was too large compared with that 
for the small values. In the first series an aperiodic electrometer 
was used, in the second a periodic instrument. It is not obvious 
from the theory that has been given why this distinction should 
be found between different experimental arrangements: for the 
only difference made in equation (21) is that a and /3 are complex 
with a periodic needle and real when the needle is aperiodic. 
But Meyer and Regener's method of observing the fluctuations 
is open to exception: they took a reading of 6' t orAy when the 
needle reversed its motion at a peak in the fluctuation curve. 
Now there is no reason that I can see for choosing the peaks for 
observation in preference to any other points on the curve: the 
effect of the various particles emitted is integrated by the instru- 
ments at the peaks in a manner no less complex than when the 
needle is moving constantly in the same direction. The only 
justification for choosing the peaks is that they are easy to observe 
(since the needle is at rest) and that they are points chosen at 
random. Now it seems likely that there might be a tendency to 
overlook peaks in the curve near the zero position of the needle, 
when the total range of the fluctuation is small, and to observe 
all the peaks which are more distant from the zero position. 
This tendency would be the more marked, the gi^eater the range 
of the fluctuations and the swifter the motion of the needle. For 
the latter reason it would be more marked with a periodic instru- 
ment than with an aperiodic, and for the former reason it would 
be more marked when the total current was large. Accordingly 
we might expect to find that, in the case of the periodic needle, 
the observed values of A^ would be too large in the case of large 
values of iV", relatively to those values for smaller values of N. This 
differentiation is what is shown in Meyer and Regener's tables. 

On the whole, Meyer and Regener's attempt to prove the form 

of the relation between A^ and -^ seems to have been fairly 

satisfactory: but criticism can be directed against their attempt 

to deduce from A^ an absolute value for -^. In the first place, 

they seem to neglect altogether the effect of the constant of the 
Bronson resistance and practically write 

A- = ^.a. 

132 Mr Campbell, The study of discontinuous phenomena. 

If their absolute value accorded well with that deduced from other 
work it can only be because p was small compared with a: but, 
for all they say, p might have been less than a, or, still worse, 
equal to a. 

Meyer and Regener also introduce a curious correction by 
extrapolation for the capacity of their electrode system. I should 
have thought that it was obvious on general grounds that the 
value of A^ was independent of the capacity as shown by (21), for 

both Ot and {Ot'^Y are inversely proportional to the capacity. 
They extrapolate for zero capacity: but, surely, if the capacity is 

zero the fluctuations must be infinite and the value of -^ infinite. 

If extrapolation is to be used at all, it would appear to be more 
reasonable to extrapolate for infinite capacity: such a process 
reduces the term in p (equation (20)), which they neglect, to zero 
— but unfortunately it reduces all other terms in the same ratio. 

Lastly, Meyer and Regener, in estimating the average value 
of A^ divide SA^ by n — \, and not by n, where n is the total 
number of observations. There seems to me a confusion here 
with the determination of the probable error of a variable given 
by a set of dependent equations from the 'residuals' of those 
equations after the probable value of the variable is substituted. 
But there seems to be no quantity analogous to 'residuals' in the 
case we are considering: the mean fluctuation is simply pro- 
portional to the mean 'error' in N. 

Geiger's method. 

§ 13. We will now proceed to the discussion of Geiger's method, 
in which no Bronson resistance was used, but the current due 
to one a ray source balanced by another current, opposite in sign 
and, on the average, equal in modulus, due to another source. 
The deflection of the needle is the algebraic sum of the deflections 
due to the two sources. 

If we consider only one source, the equations corresponding 
to (8) and (5), giving the deflection of the needle at all times 
after one or m particles respectively^ have been emitted from that 
source, can be found directly from those equations by putting 
p = 0. Hence, using the same notation as before, 

e = A.e-'^' + B^e-^' + P^ (24), 

Where ^^ = 0/7 ^^ = ^^ «3^ ' ^^^'^^^i:^' 

and dT = tlZ^ {A,e--'>-' + B,e-'^*r' + p^) (25) 

= 2;:;'^i^(0(Bay) (26). 

Mr Campbell, The study of discontinuous phenomena. 133 

§ 14. Let the suffix + denote in all cases quantities corre- 
sponding to one source, and the suffix — denote quantities corre- 
sponding to the other source. Then, it is clear that (10) may be 
replaced by 

where ^+p (r) and <^_p (r) may have any of the possible values 

Nt-Vx^^,...,Nt + x^n, or -NT + x^^,...,-NT-\-x+n respectively, 

for we must remember that Nj^ = — N_. 

Reasoning in precisely the same way as before, we arrive at 
the following equation corresponding to (13), 

s, {d^T + e_Ty = Kli F' (^^) sj=i ^+p ^-p (^+'- + ^-)' (28). 

Now 'fZ^ ^+p ^-p {x+r + ^-r)^ is the average value of {x^^ — x^rY 
for a very large number of values of that quantity. But by a 
well-known theorem in probability, the average value of {a + 6)^ 
is a? + 6^ if a and h are independent. But the average of a?+/ 
and of x_r^ is the same and equal, by (1), to INt. Hence, we get 
in place of (15), 

^t.{d^T-^0_Tf = ^Nr^dtF"^{t) (29) 

or Il'^ = 2N{uT+v){sd.y) ' (31). 

Now, since A'^ is dependent on T, we cannot compare directly 

values of A' for different values of T. That is to say, if we record 

photographically, as suggested in § 10, the values of A'^ for all 

values of T, we cannot put 2iV^oc (average of all these values 

of A'^). We must compare values of A'^ for different values of T 

by dividing each value of A'^ by the appropriate value of {uT -\- v), 


and then take the average of —f=^ . We cannot even, as might 

° uT+v 

appear at first sight, take the difference of values of A' for a series 

of times differing by T and equate the average of the squares of 

these differences to 2iV {uT + v) : for such a procedure would involve 

the false proposition that 

|A/-A/|^ = A/2-A%. 

Accordingly the labour of deducing the value of iV from the 
observed fluctuations will be very much greater than in Meyer 
and Regener's method, for it would be difficult to construct a 

134 Mr Campbell, The study of discontinuous phenomena. 

mechanical integrator which should give the value of \-. — - — rrdx 
for a wholly irregular curve. 

§ 15. As regards the choice of instruments for this method, 
the conclusions reached in considering Meyer and Regener's 
method are still valid. Since p is zero there is no need for 
considering the relation between the periods of the electrometer 
and the resistance, but it is still desirable that a should be very 
large. For there is some uncertainty in the determination of the 
value of this quantity : since the importance of the terms involving 
a in comparison with the term Pi^T, which does not involve a, 
decreases as a increases, it is clearly desirable to make a as large 
as possible, that is, to use an electroscope with as short a period 
as possible. 

On general grounds Geiger's method seems less satisfactory 
than that of Meyer and Regener for observations on phenomena 
for which both methods are, in principle, equally applicable. But 
it is easy to imagine circumstances in which Geiger's method 
would, and Meyer and Regener's would not, be applicable : for 
instance, the object of the experiment might be to detect dis- 
continuity in the difference between two sources, and indeed 
I am engaged at present in endeavouring to conduct such 
experiments. It is desirable, therefore, to consider Geiger's 
method a little more closely. 

I 16. It must be pointed out that the theory of Geiger's 
method which has just been elaborated does not represent any 
practicable experimental conditions. It is impossible to reduce 
the quantity p accurately to zero. In the first place, there is 
always an ' insulation leak,' which acts like a Bronson resistance 
and sets a limit to the deflection which the indicating instrument 
will attain when acted upon for an infinite time by a finite current. 
But this leak can (though with great difiiculty) be made so small 
that values of T can be chosen such that aT is very large and 
pT is very small. In such a case Geiger's method could be applied 
according to the theory just given. But, in most of the cases to 
which the method is likely to be applied, there is also an ' apparent 
insulation leak,' which is a far more serious matter. It must 
be remembered that no ionisation current is really perfectly 
'saturated.' A condition can often be attained ia which an 
increase of the acting potential difference from 1000 to 2000 volts 
does not increase the current by more than O'OOl of its value, but 
this does not prove that an increase of 1 volt in the p.d. may not 
cause an increase of one millionth in the current. And a change 
of one millionth may be extremely important when we are 
concerned with the minute differences in the magnitudes of two 

Mr Campbell, The study of discontinuous phenomena. 185 

balanced currents very nearly equal. The effect of a lack of 
perfect saturation is to diminish the current due to either source 
when the potential of the electrode is of the sign corresponding 
to a preponderance of the current due to that source : it sets a 
finite limit to the potential which the electrode can attain, 
diminishes the magnitude of the fluctuations and, in every manner, 
acts like an insulation leak. 

Errors from this source, even if their possibility had occurred 
to me, would have been rejected as unimportant, if I had not had 
actual experience of them. I have found the false insulation leak 
a very serious trouble in dealing with currents for which saturation 
is likely to be far easier of attainment than in the case of a ray 
currents ; these currents are those due to the photoelectric effect 
in a very high vacuum. In dealing with these currents, the 
saturation, tested by the ordinary method, is perfect at 50 volts : 
tested by balancing two currents and then watching the decay 
of a potential difference applied to the common electrode, saturation 
is not perfect even with a p.d. of 500 volts, though it is much 
more nearly perfect than at 50 volts. 

The existence of this false insulation current leak reduces 
Geiger's method to that of Meyer and Regener. p has a finite 
value which can be found by watching the decay of a p.d. given 
to the electrode when the two currents are balanced. It should 
be pointed out that this apparent insulation leak affects Meyer 
and Regener's experiments also : in that case too the value of p 
must be found when the current to be measured is flowing through 
the Bronson resistance and the compensating P.D. applied. 

§ 17. A few remarks on Geiger's work are all that remains. 

(1) In the first place we may note that by taking some 
100 observations only of the fluctuations Geiger, like Meyer and 
Regener, introduced a probable error of some 10 7o- Since the 
agreement which he found between theory and experiment was 
of this order of accuracy, it might seem that in other respects 
his work was satisfactory. But 

(2) It seems to me that Geiger employed a totally inadequate 
and inaccurate theory in the interpretation of his observations. 
He assumes, like Meyer and Regener, that the value of his 
fluctuations depends only on the constants of his instruments, 
but equation (33) shows that it is also a function of the time 
of observation. Only the most general consideration is necessary 
to show that in Geiger's method (assuming the absence of an 
important insulation leak) the effects of the particles which came 
off at a distant time are as important as the effects of those which 
came off only just before the moment of observation: the mean 
value of the fluctuations over any short period must depend upon 
the distance of this period from the time when the electrode was 

VOL. XV. PT. II. 10 

136 Ml' Campbell, The study of discontinuous pheiiomena. 

insulated. But Geiger adds all his fluctuations together, whatever 
the time of observation, as if they were comparable. 

Accordingly it appears to me that Geiger's expectation of 
obtaining a result even in approximate accordance with that 
predicted by other work was justified only if he had a large 
false insulation leak.' If there is such a leak, then Geiger's 
method is reduced to that of Meyer and Regener, and all observa- 
tions at more than a certain distance from the moment of 
insulation are comparable. The existence of an insulation leak 
would also explain that the 'time of swing of the needle' (o| sees.) 
is so much smaller than that which is found with most Dolezalek 
electrometers : for the period between two peaks might then 
depend, not on the vibrations of the needle, but on the period 
of decay of his quasi-' Bronson -resistance.' But, if this suggestion 
is correct, he neglected totally the real time of swing of his needle. 

(3) As a minor point we may note that Geiger, attempting 
to use von Schweidler's theory, puts j A' | = \/Ni. Correctly 

I A' I = A / — - for one source of rays and 2 a/ — for 2 inde- 
pendent sources (error about 20 ''/J. The quantity which should 
be equal to '^Nt is v A'^. As I have pointed out, it seems 
impossible to find a complete expression for the value of | A' | 
in terms of N and the instrumental constants. 

In view of these sources of error, it is difficult to avoid the 
conclusion that the close agreement found by Geiger between 
prediction and experiment was mainly fortuitous. 

In conclusion I must offer my best thanks to Mr G. H. Hardy 
for his invaluable help in §§ 5 — 8 : the main principle of the 
argument is his rather than mine ; to Sir J. J, Thomson, who 
has pointed out several errors in the original calculations; and 
also to Mr T. H. Laby, whose acute criticism first turned my 
attention to the subject and aided greatly in the attainment of 
clear ideas. 


§§ 1 — 3. A slight modification and generalisation of von 
Schweidler's theory of the fluctuations in the emission of rays 
by a radioactive substance. 

§§ 4 — 7. A consideration of the theory of Meyer and Regener's 
experiment based on von Schweidler's work. 

§§ 8 — 12. Application of this theory to experimental arrange- 

§§ 13 — 17. The theory of Geiger's experiment in the same 

Miss Wheldale, On the nature of anthocyanin. 137 

On the nature of anthocyanin. By Miss M. Wheldale, 
Newnham College. (Communicated by Professor Bateson, F.R.S.) 

[Read 8 March 1909.] 

Many investigators have suggested, from time to time, that 
a relationship exists between the widely distributed tannins in 
plants and the equally widely distributed pigment known as 
"anthocyanin," Curtel\ Dennert^ Gautier^ Ichimura*, 
MIRANDE^ Newbigin^ Wiesner^ Wigand^ and ZoPF^ among 
others, mention the occurrence of a colourless chromogen, of the 
nature of a tannin, in tissues, which eventually may become 
coloured with anthocyanin; the colouration arises under the 
influence of various agents, such as nutrition, temperature, light, 
and injury, either mechanical or such as is brought about by 
attacks of fungi, etc. The process of transition, moreover, from 
chromogen to pigment has been regarded as one of oxidation. 

Not only has the above relationship been established, but the 
view has also been held that anthocyanin itself is some compound 
of a tannic acid. 

Overton^", for instance, from the increased production of 
anthocyanin brought about by artificial feeding of plants with 
carbohydrates, arrived at the conclusion that this pigment may 
very possibly be a sugar compound of a tannic acid, that is a 

Gautier^^ also isolated various colouring matters from the 
red leaves of the Yine and he regards these pigments as coloured 
tannic acids. 

Pfeffer^^, in a general review of the subject, states that the 
red and blue pigments dissolved in the cell-sap, such as anthocyanin, 
seem to be tannins or compounds allied to phenols, though in his 
view they may also be derived from other substances since they 
often occur in plants which contain no tannin. 

Heise^^ in addition, isolated two pigments from the Bilberry 
and showed one to be the glucoside of the other. Both substances 
appear to be aromatic compounds though they have not directly 
been proved to be tannins. 

The word tannin is a somewhat difficult term to define; 
it is used in general for a class of substances very widely 
distributed in plants and having certain properties in common. 


138 Miss Wheldale, On the nature of anthocyanin. 

Their characteristics, as given in most text-books, are an astringent 
taste, the production of a blue or a green colour with iron salts, 
tanning properties with animal membranes, power to precipitate 
albumin and gelatine, etc., etc. The exact constitution of the 
tannins is also rather indefinite though it is obvious that they are 
aromatic compounds of the benzene series. Broadly speaking 
tannins include numerous tannic acids, such as gallic, gallotannic, 
catechinic, caffeic, protocatechuic, diprotocatechuic, ellagic, quer- 
citannic, etc., usually existing in plants in the form of glucosides, 
i.e. ethereal compounds with various sugars or with the trihydric 
phenol, phloroglucin. 

It has been suggested that tannins may be divisible into 
two groups, derived respectively from a dihydric phenol, such 
as pyrocatechol, and a trihydric phenol, such as pyrogallol. The 
kind of relationship might be illustrated as follows : — 

C6H4(OH)2 CeH3(OH)2.COOH C6H3(OH)2 . CO . . CeHg . OH . COOH 

pyrocatechol protocatechuic acid diprotocatechuic acid 

C9H3(OH)3 C6H2(OH)3 . GOGH CoHalOHjs . CO . . C6H2(OH)2 . COOH 

pyrogallol gallic acid tannic acid or digallic acid 

The tannins included in the first group give as a rule an 
iron-greening reaction (though this is by no means invariably 
the case), produce pyrocatechol on dry distillation and proto- 
catechuic acid when fused with caustic alkali. Those of the 
second group give an iron-blueing reaction, produce pyrogallol 
on dry distillation and gallic acid on fusion with caustic alkali. 

Waage" and also Nickel^^ are of the opinion that another 
series of tannic acids arises from the oxidation of phloroglucin, 
the isomer of pyrogallol : — 

G6H3(OH)3 C6H2{OH)3 . COOH C6H2(OH)3 . CO . . C6H2(OH)2 . COOH 

phloroglucin phloroglucin carbonsaure phloroglucin gerbsaure 

(carboxylic acid) (tannic acid) 

Hence there may well be a complexity of tannins of different 

With a view to finding out whether, and if so, in what way 
anthocyanin is related to tannin, the extracts from flowers of 
numerous natural orders, both with and without anthocyanin, 
were tested for tannin with various reagents. Although the 
behaviour of the pigments has been diverse in many ways, 
a certain amount of classification can be based on the results 

It must at the same time be borne in mind that some of 
the reagents used in these tests, react not only with the tannins 
but also with many other bodies, such as phenols and their 
numerous derivatives. 

Miss Wheldale, On the nature of anthocyanin. 139 

The reagents* employed were as follows: — 

(1) Strong bases, such as solutions of caustic potash or soda 
and of ammonia. 

(2) Lime water. A blue, brown or red colour or precipitate 
shows tannins. 

(3) Strong acids, such as sulphuric, hydrochloric and nitric 
acids. The reactions of Brissemoret^^ are interesting in this 
connection though they have not been employed to any great 

(4) Iron salts. Ferric chloride solution was used and also 
a solution of ferrous sulphate, in which some oxidation to the 
ferric salt has taken place. A blue-black or dull green colouration 
shows tannins. 

(5) Precipitation by basic lead acetate which precipitates 
most tannins and glucosides. 

(6) Potassium ferricyanide solution and ammonia. A reddish- 
brown colouration changing to brown shows tannins. 

(7) Uranium acetate solution. A brown precipitate or 
reddish-brown or brown colour shows tannins. 

(8) Ammonium molybdate solution, both alone and with the 
addition of a saturated solution of ammonium chloride. According 
to Gardiner"!* alkaline molybdate gives a red colour with tannin. 
If excess of ammonium chloride is added, a voluminous yellow 
precipitate is produced. Moreover by means of this reagent, 
according to the above author, tannin may be readily separated 
from tannic, i.e. digallic acid, for whereas the compound of tannin 
and molybdate (?) is insoluble in ammonium chloride, that with 
tannic acid is soluble. The reagent therefore separates the 
glucoside tannins from tannic acid. 

As a preliminary statement it may be said that tannins, like 
that of the oak gall, giving an intense blue-black colour with iron 
salts and also reactions 2, 6, and 7 are rare among herbaceous 
plants. There are however widely distributed among the latter, 
certain colourless or slightly yellow substances, giving an iron- 
greening reaction though they are not typically tannins, since 
they do not as a rule give reactions 2, 6, 7, and 8. These substances 
are characterised in addition by the bright yellow colour produced 
when they are acted upon by strong bases and by lime-water. 
They give the same colour also with strong mineral acids, such 
as sulphuric and hydrochloric, and they are precipitated by basic 
lead acetate as canary-yellow precipitates. 

These reactions are best seen when extracts of white flowers 
are used or those of 3^ellow flowers, in which the colour is due 
to plastid pigment only. Flowers giving these reactions are 
arranged in the following scheme. 

* Darwin and Acton, Physiology of Plants. t (iardiuer ". 

140 Miss Wheldale, On the nature of anthoci/anin. 

I. White flowers, of which an extract ogives a bright yellow 
colour with alkalis and acids, a bright yellow precipitate with 
basic lead acetate and a reaction with iron salts. 

(a) Those giving a green colouration with iron salts : 
Mesemhryanthenium Haworthii, Golchicum sp., Nerine flexuosa, 
paper white variety of the polyanthus Narcissus, white berries 
of Si/mphoricarpus raceniosus, white variety of Chrysanthemum 
carinatiim, white variety of autumnal cultivated Ghri/santhemum, 
ivory white variety of Viola tricolor, white variety of Ahutilon 
striatum, Erica Bowieana and white variety of Primula sinensis. 

{h) Those giving a blue colouration with iron salts : None. 

II. Yellow flowers (albino as regards anthocyanin, but with 
yellow plastid pigments), of which the extract gives the same 
reactions as those in I. 

(a) Those giving a green colouration with iron salts: 
Ivory variety of Helianthemum vulgare, Calendula officinalis, 
yellow variety of autumnal cultivated Chrysanthemum, Erigeron 
Canadensis, Gaillardia sp., Gazania splendens, Helenium iiudiflorum, 
Helianthus annuus, Picris paucifiorus, Senecio Jacohaea, pale and 
deep yellow varieties of Zinnia elegans, Hypericum Hookerianum, 
Spartium junceum, Linum flavum, Bartonia aurea, yellow variety 
of Ahutilon striatum, Jasminum nudiflorum, Argenione grandifiora, 
Eschscholtzia Californica, PHmula Kewensis, Potentilla fruticosa, 
Hyoscyamus chloranthus, yellow variety of Salpiglossis grandijiora, 
calyx of Physalis alkekengi, pale and deep yellow varieties of 
Tropaeolum majus, Tropaeolum canariense, and pale and deep 
yellow varieties of Viola tricolor. 

(6) Those giviug a blue colouration with iron salts : 
Alyssura maritimum. 

Exceptions were the following, which give a yellow precipitate 
with basic lead acetate, a yellow colour with alkalis but not the 
above reactions with iron salts: Taraxacum officinale^, Brassica 
sinapis*, Cucurbita Pepo*, and fruit oi Lycopersicum esculentum. 

It might be noted that these exceptions are chiefly plants 
which do not normally produce anthocyanin. 

The xanthei'c pigments of many yellow flowers seem to be 
very similar in nature to the substances present in the above 
Classes I. and II. They differ in that the yellow extract usually 
deepens to orange-yellow or red with alkalis and acids and the 
precipitates with basic lead acetate are of corresponding shades. 
The iron reaction is usually green. Class III. contains genera 
whose flowers give these reactions. 

* Tested only with ferric chloride which does not always give a satisfactory 

Mij:>f> W/ieldale, On the iiatLire of anthocyanin. 141 

III. Yellow flowers containing a so-called xanthe'ic pigment 
(sometimes in addition a yellow plastid pigment), of which the 
extract gives a colouration with iron salts; a yellow, orange-yellow, 
orange or red precipitate with basic lead acetate and similar 
colourations with acids and alkalis. 

(a) Those giving a green colouration with iron salts : 
Mesembryanthemum pomeridianmn (yellow)*, Centaurea eriophora 
(orange-yellow), Centaurea scabiosa (orange-yellow), yellow variety 
of Chrysanthemum carinatum (orange), Gorydalis lidea (orange- 
yellow), yellow variety of Dahlia variabilis (red), yellow variety 
of Helichrysum bracteatum (orange), Tagetes signata (orange), 
Goronilla glauca (orange), Mirabilis Jalajja (yellow), Primula 
acaulis (orange). Calceolaria sp. (orange), and Nemesia stru7nosa 

(6) Those giving a blue colouration with iron salts : 
Linaria multipunctata (orange-red) and Linaria vulgaris (orange- 
red). The following are exceptions in that they do not give the 
above reactions with iron salts: Coreopsis Drummondii'f (red) and 
Verbascum Lychinitis (yellow). 

When anthocyanin was present in the genera examined, the 
reactions given by the usual reagents were diverse, but the more 
common type of reaction is that given in Class IV., i.e. a green 
colouration with alkalis, a green precipitate with basic lead acetate 
and a green or blue colouration with iron salts. It is doubtful 
whether the blue colouration given by the anthocyanin of many 
herbaceous genera is in any way similar to the true iron-blueing 
tannin reaction. Extracts from the flowers of some shrubs, such 
as red varieties of Rosa, give a true iron-blueing reaction like that 
of the oak-gall, and this result may be due to admixture of tannin 
present in the plant. I am inclined to believe that the iron-blueing 
reaction of the flower extract of herbaceous plants may only be 
a specific reaction of anthocyanin itself and not an indication 
of a true tannin nature of this substance. Yet this point of view 
by no means vitiates the suggestion that this pigment may be an 
aromatic substance closely allied to the tannins. 

The anthocyanin of Glass IV. is of the purple or purplish-red 
type. Though the colours of the flowers, from which it is obtained, 
often differ among themselves, the alcoholic extracts have the 
common property of being purple or purplish-red in colour. 

IV. Red, purple or blue flowers containing anthocyanin 
(sometimes in addition plastid pigment), of which the extract 
gives a green colour with alkalis and a green precipitate with 
basic lead acetate. 

* Denotes colour given with allialis and basic lead acetate. 
t Tested only with ferric chloride. 

142 3Iiss Wheldale, On the nature of anthocyanin. 

(a) Those giving a greea colouration with iron salts: 
Blue Vinca major and blue Campanula' sp., carmine pericarp 
of Euonymus europaeus, blue Tradescantia virginiana, blue Aster 
tripolium, blue and magenta varieties of Cineraria sp., crimson, 
mauve, and purple varieties of autumn Chrysanthemum, crimson 
Hieracium ruhrum, magenta variety of Helichrysum hi^acteatum, 
pink and scarlet varieties of Zinnia elegans, mauve Auhrietia 
graeca, brown Cheiranthus Cheiri, pink Epacris pulchella, carmine 
Salvia didcis, purple Salvia Horminum, purplish-red Salvia 
involucrata, blue Anemone coronaria, carmine Tropaeolum speci- 
osum, purple varieties of Viola tricolor. 

(h) Those giving a blue colouration with iron salts : 
Orange Alstroemeria aurantiaca, magenta Impatiens episcopi, 
crimson Helianthemu7n vulgare, pink Echeveria retusa, magenta 
Azalea amoena, floral bracts of Euphorbia splendens, carmine 
leaf bracts of Euphorbia pulcherr^ima, crimson Goronilla viminalis, 
orange Lilium Tigrinum, crimson Abutilon striatum, purple 
Fuchsia sp., black berries of Rosa pimpinellifolia, black berries 
of Atropa Belladonna, magenta Petunia violacea. 

From the above classification we may conclude that among 
herbaceous plants aromatic substances giving an iron-greening 
reaction are common. An iron-blueing reaction however is rare 
when anthocyanin is absent, but more common when this pigment 
is present, though it is probable that the reaction in the latter 
case does not indicate a true tannin nature for this substance. 

When a species is in type anthocyanic with an albino variety 
(as regards this pigment), for example Chrysanthemum, Viola, 
Abutilon, Helianthemum, Zinnia and Helichrysum, then with 
alkalis the albino extract is coloured yellow and that of the 
anthocyanic type blue with a small amount of alkali but green 
with excess. Similarly the albino extract gives a yellow precipitate 
with basic lead acetate, and that of the type a green precipitate. 
The iron reaction is usually the same for both type and variety, 
though in the case of Helianthemum and Abutilon, the iron 
reaction is green for the non-anthocyanic varieties but blue for 
the anthocyanic type. 

A possible explanation for the reactions observed might be 
as follows: — That many plants free from anthocyanin, and also 
albino varieties of anthocyanic types, contain colourless aromatic 
chromogens, probably often in combination with sugars as 
glucosides as suggested by Overton^". These chromogens appear 
to have acid properties and usually give an iron-greening reaction ; 
as present in the plant in the undissociated state they are almost 
colourless, but on addition of strong alkali a dissociable salt is 
formed, of which the anion is bright yellow. The yellow colour 
disappears again on neutralisation with acid, so that the reaction 

Miss Wheldale, On the nature of anthocyanin. 143 

resembles that of an acid-alkali indicator. With heavy metals, 
such as copper and lead, insoluble coloured salts are formed. 

There appears to be evidence, as will be discussed later, that 
the production of pigment in anthocyanic species is brought about 
through the agency of an oxydase so that anthocyanin may be 
regarded as a coloured oxidised product of an aromatic chromogen 
and moreover, like the unaltered chromogen, as an acid capable 
of producing salts. In the acid state the molecule of anthocyanin 
is red but the addition of alkali produces a blue salt. 

We may suppose that there is usually unaltered chromogen 
present in the plant in addition to anthocyanin, and the simul- 
taneous existence of these two bodies would account for the green 
colour given by alkalis and the green precipitate by basic lead 
acetate, i.e. a mixture due to the blue salt of the oxidised product 
and the yellow salt of the chromogen. The stronger — more 
oxidised — acid would probably react first with bases; hence the 
blue colouration with a slight amount of alkali. 

On this supposition, the green precipitates prepared and 
analysed by Heise^^ and Gautier" represents a mixture of the 
salts of both anthocyanic acid and its chromogen. 

An alternative explanation is that offered by Overton^", who 
regards anthocyanin as a di- or poly-basic acid, the blue colour 
given by a small amount of alkali being due to the acid salt, the 
green colour with excess of alkali to the neutral salt. 

Grafe^^ too, is of the opinion that one of the pigments 
isolated by him from Althaea rosea is a di-basic acid; he regards 
the green colour with alkalis as a specific reaction of anthocyanin 
and not one due to admixture with any other substances giving 
a yellow reaction. 

Evidence for the assumption that the aromatic chromogen 
forms a component of anthocyanin has been arrived at through 
experiments in cross-breeding*. It appears, from this source, 
that the components of anthocyanin can be represented by various 
Mendelian factors, the loss of which gives rise to derivative 
varieties. In Antirrhinum majus, an ivory-white variety exists, 
which is free from anthocyanin, but contains a chromogen such 
as those described above. The magenta type contains anthocyanin. 
It has been proved experimentally that the factor representing 
the chromogen is essential to the constitution of the magenta 

Cross-breeding with Antirrhinum shows moreover that the 
so-called xantheic pigment of the yellow variety is essential to 
the constitution of the ivory-white and is hypostatic to it. In 
fact xanthein appears to be a yellow aromatic chromogen in a 

* Wheldale 19. 

14-4 Miss Wheldale, On the nature of antliocyanin. 

lower stage of formation than the ivory-white, yet capable, like 
the latter, of being acted upon by the oxydase with the productions 
of anthocyanin, which in this case is mixed with unaltered yellow 
chromogen and consequently produces the crimson colour of the 
crimson variety. 

Antirrhinum is the type of a number of genera in which 
the colourless chromogen of the ivory-white variety gives rise, 
probably through loss of some factor, to a xanthe'ic pigment. 

Definite knowledge as to the nature and constitution of these 
aromatic chromogens, from the oxidation of which anthocyanin 
may arise, is a difficult chemical problem. I am inclined to 
believe that they belong to the flavone and xanthone classes 
of natural colouring matters*, which they closely resemble in 
properties and reactions. The flavones and xanthones are chiefly 
present in plants as glucosides or rhamnosides, most have fifteen 
carbon atoms in their empirical formulae and on fusion with 
caustic alkali many give protocatechuic acid and phloroglucin. 

The nucleus of these substances is 7-pyrone, which may be 
regarded as an anhydride of a diolefine-dioxyketone : — 

CH = CH 
CH = CH 

Xanthones and flavones are derived from pheno-7-pyrone : — 



Xanthone being a dibenzopyrone 


See Czapek, Biochemie der Pjianzen. 

Miss Wheldale, On the natm^e of anthoci/anin. 145 

and flavone a ^-phenyl-benzo-7-pyrone : — 

Among those of other investigators, the very valuable researches 
of Peekin^I""*" and his colleagues on the yellow colouring matters 
of plants in connection with their dyeing properties, have thrown 
much light on the constitution of these bodies, and since they are 
of great importance in connection with this point I propose giving 
a short account of the properties and constitution of the chief 
members of the group, as well as their distribution among various 
natural orders. The xanthones appear to be less widely distributed 
than the flavones and it is to the latter that most importance 
may be attached. 

Most of the colouring matters may be regarded as arising 
from a hydroxy-derivative of flavone : — 




Generally speaking they are yellow crystalline bodies, not very 
soluble in water in the free state, more soluble probably as 
glucosides. They are soluble in acids giving yellow, orange or 
red solutions, and in the absence of water many form crystalline 
compounds Avith a molecule of the acid, these same compounds 
being again decomposed into acid and colouring matter on addition 
of water. At the same time they appear to have basic properties ; 
in alkalis they are soluble, giving again yellow, orange or red 
solutions. Many, moreover, are able, in the absence of water, 
to withdraw potassium from potassium acetate, with the formation 
of a mono-potassium salt. They are precipitated by lead acetate 
as yellow, orange or red precipitates and with ferric chloride 
solution they usually give a dull green colouration, occasionally 
reddish-brown. The decomposition products on fusion with alkali 
are frequently phloroglucin and protocatechuic acid, though some- 
times resorcinol, resorcylic or hydroxybenzoic acids are formed 

146 Miss Wheldale, On the nature of anthocyanin. 

according to variations in the constitution of the colouring matter. 
With aniline or toluidine nitrate and potassium nitrite they give 
a cinnabar-red precipitate. In the plant the flavones mostly occur 
as glucosides, the sugar being rhamnose or glucose. 

Quercetin C15HJ0O7 is very widely distributed. It may be 
regarded as a pentahydroxy flavone : — 






Quercetin occurs free, that is not as a glucoside, in many plants. 
The following are interesting examples: — its occurrence in flowers 
of Prunus spinosa, Crataegus oxyacantha, Delphinium Zalil, and 
Cheiranthus Cheiri; in leaves of Rhus I'hodanthema, R. metopium, 
Ailanthus glandulosa, Goriaria myrtifolia, Calluna vulgaris; it 
exists also in the outer bulb scales of Allium cepa and in many 
other plants. 

On fusion with caustic alkali, quercetin gives protocatechuic 
acid and phloroglucin derived from the catechol and phloroglucinol 
nuclei respectively. 

In many plants on the other hand it is combined with glucose 
or rhamnose as glucosides. It occurs as 'osyritrin'; a glucose 
glucoside, in leaves of Osy7'is compressa; 'osyritrin' is also identical 
with the 'viola quercitrin' of flowers of Viola tricolor variensis and 
with 'myrticolorin' in leaves of Eucalyptus macrorhyncha. Again 
with one molecule of rhamnose it occurs as the glucoside 'quer- 
citnji' in the bark of QuerciLs tinctoria and with two molecules of 
rhamnose as 'rutin' in Ruta graveolens. The flowers of Viola 
odorata and TrifoUum repens also contain quercetin in the form 
of a glucoside. 

Morin, C15H10O7, occurring in the wood of Morus tinctoria and 
Artocarpus integrifolia, may be regarded as an isomer of quercetin 
containini/ the resorcinol instead of the catechol nucleus : — 






On fusion with alkali it gives /3-resorcylic acid and phloroglucin. 

Miss Wheldale, On the nature of anthocyanin. 


Rhamnetin, CifiHi207, a rnonomethyl ether of quercetin is found 
as a rhamnose glucoside — ' xanthorhamnin' * — in fruits of Rhamnus 
spp. Its constitution may be represented as : — 



Isorhamnetin, CisHjgOy, an isomerous monomethyl ether, occurs in 
the flowers of Gheiranthus cheiri and oi Delphinium Zalil: it may 
be represented as : — 





Rhamnazin, C17H14O7, a dimethyl ether of quercetin, occurs as a 
glucoside in addition to xanthorhamnin in the fruits of Rhamnus 
spp. ; it may be represented as : — 



onr Y \ — <r %0H 

Fisetin, CigHjoOe, occurs in the wood of Rhus cotinus, R. coriaria 
and R. rhodanthema. 

It differs from quercetin in containing a resorcinol instead of 
a phloroglucinol nucleus and may be regarded as a tetrahydroxy 
flavone : — 

OHf/ Y V-<^ ^OH 



Hence on fusion with caustic alkali, the decomposition products 
are protocatechuic acid and resorcinol, 

* Cp. " On some points in the Histology and Physiology of the Fruits and Seeds 
oi Rhamnus." H. Marshall-Ward and J. Dunlop, Ann. Bot. Vol. i. 1887-8. 

148 Miss Wheldale, On the nature of anthocyanin. 

Luteolin, CigHjoOe, is found in Reseda luteola and Genista 
tinctoria. It is an isomer of fisetin and may be represented as : — 




On fusion with alkali, phloroglucin and protocatechuic acid are 

Myricetin, CigHmOg, is found in the bark of Myrica nagi, in the 
leaves of Rhus coriaria and R. cotinus, R. metopium, Pistacia 
lentiscus and others. It may be regarded as a hydroxyquercetin 
containing a pyrogallol instead of a catechol nucleus : — 







Hence on fusion with caustic alkali it gives gallic acid and 

Chrysin, Ci5Hio04, is found in buds of Populus sp. It is a 
dihydroxy flavone : — 




Apigenin, dgllioOg, occurs in the form of a glucoside — 'apiln' — 
in the leaves, stem and fruit of Parsley, Apiinn petroselium. It 
may be regarded as a hydroxy chrysin or trihydroxy flavone : — 




On fusion with caustic alkali, the decomposition products are 
phloroglucin and parahydroxybenzoic acid. 

Miss Wheldale, On the nature of anthocyanin. 


Kampherol, G^JiioOg, occurs as a rhamnose glucoside Wohinin' 
in the flowers of Robinia pseudacacia, and also as another glucoside 
in the flowers of Delphinium consolida and Prunus spinosa. It 
may be regarded as a connecting link between apigenin and 
quercetin : — 
















On fusion with caustic alkali it gives parahydroxybenzoic acid 
and phloroglucin. 

The above account conveys some idea of the wide distribution 
of the flavone series of colouring matters. Some fifty to sixty 
genera have been examined by Perkin and his colleagues and 
these genera are members of many different natural orders. 
Several of the flavones are common to genera by no means 
closely allied and again others, as far as his investigations have 
gone, are apparently specific. The constitution of these bodies, 
as given above, shows that there is great scope for slight variations 
and many isomeric forms may exist and may be specific for different 
plants. At the same time the general nature and tendencies of 
these bodies are similar, and it is not difficult to conceive of their 
acting as chromogens in the formation of the various kinds of red 
pigments found in plants. 

I have repeated the method of extraction of Perkin and 
HuMMEL^^ for quercetin from onion skins and I find this body 
very similar in its properties and reactions to the aromatic 
chromogens present in flowers. Sometimes these bodies crystallise 
out from the flower extract as in Narcissus Tazetta*, Eschscholtzia, 
and Viola'f in which case the substance is more easily prepared 
in its pure state. The yellow crystalline pigment of Viola is 
without doubt the 'viola quercitrin' of Perkin. 


t Wheldale 20. 

150 Miss Wheldale, On the nature of anthocyanin. 

The flowers of the original type in Narcissus Tazetta owe 
their colour to the presence of several pigments ; the lemon 
yellow of the perianth segments is due to plastids containing 
xanthin, and the orange yellow of the corona to plastids containing 
both xanthin and carotin. In addition, all parts of the flower 
contain a yellow flavone pigment which crystallises from the 
extract in clusters of yellow needles. To ascertain something 
of its nature, this yellow crystalline pigment was fused with 
caustic alkali, the melt dissolved in water, neutralised and 
precipitated with basic lead acetate. The precipitate on de- 
composition with sulphuretted hydrogen and extraction with 
ether, gave a crystalline body having the properties of proto- 
catechuic acid. The ether extract also gave evidence of the 
presence of phloroglucin. Hence there is little doubt that the 
Narcissus pigment may be placed in the flavone series. 

A white variety of the same Narcissus has no plastid pigments 
but a pale yellow non-crj'stallisable flavone having the usual 
characteristics. On fusion with caustic alkali, phloroglucin and 
parahydroxybenzoic (?) acid were detected as decomposition 
products. Hence the flavone of the variety must differ in 
constitution slightly from the crystalline flavone of the type. 

A second variety has the crystallisable flavone only in the 
perianth, while the corona contains carotin, 

A third variety contains a non-crystallisable flavone and 
xanthin in addition in the corona. 

In a similar way the non-crystallisable chromogen from the 
white flowers of Primula stellata and P. sinensis was isolated 
and fused with alkali. The ether extract contained phloroglucin 
and another body, very probably parahydroxybenzoic acid, since 
it gave a red precipitate with aqueous iodine and caustic potash, 
which became yellow on addition of acid. 

The work of Naylor and Chappel^^ on Rosa gallica forms 
an additional confirmation of the above suggestion as to the 
nature of the aromatic chromogens. These authors isolated from 
the petals of the above species of Rosa a yellow crystalline colouring 
matter, giving an orange-red precipitate with lead acetate and 
a brownish-black colouration with ferric chloride. 'It was soluble 
in caustic potash to a yellow or orange brown solution and in 
sulphuric acid to an orange-yellow liquid. 

Fused with caustic potash it gave phloroglucin and proto- 
catechuic acid. 

Heise^^ also found protocatechuic acid as a decomposition 
product from the fusion with alkali of one of the anthocyanic 
pigments isolated by him from the Bilberry, 

If the existence of a colourless chromogen as a precursor of 
'anthocyanin' be accepted, it is possible that the recent work 

Miss Wheldale, On the nature of anthocyanin. 151 

of Palladin^' may throw light upon the method of production 
of the pigment from its chromogen. The above author maintains, 
on the evidence of Bertrand^*, that oxydases can only oxidise 
aromatic compounds of a certain constitution, and since the 
products of oxidation may be coloured Palladin terms such 
oxydases 'pigment-building.' He further maintains that chromo- 
gens are present in many plants ; for he found that if the 
extracted sap of such plants be heated sufficiently to destroy 
the enzymes existing in the plants themselves, then the addition 
to the extracted sap of a small quantity of the peroxydase of 
Chodat and Bach^^^'^'^^^ together with a few drops of hydrogen 
peroxide, produces a purple, red or reddish-brown colouration. 

As to the constitution of the chromogen, Palladin ■^^ suggests 
that the evidence of Overton" points to the chromogen as being 
an aromatic substance combined with sugar and of this nature are 
glucosides. To quote Palladin: — "Die vorstehend beschriebenen 
Versuche und ebenfalls diejenigen Overton ergaben, dass 
verschiedene Zuckerarten ein Material darstellen, aus welchem 
verschiedenartige Atmungschromogene gebildet werden. Auch 
Glukoside konnen wahrscheinlich als Material fiir die Bildung 
der Chromogene dienen, wie es auch Overton vermutete. 
Zugunsten dieser Voraussetzung spricht der Umstand, dass die 
meisten pflanzlichen Glukoside Verbindungen verschiedener 
Zuckerarten mit aromatischen StofFen sind : nach den gegenwartig 
bekannten Tatsachen sind auch Atmungschromogene nichts anderes 
als aromatische Verbindungen. Die aromatischen Spaltungs- 
produkte der Glukoside liefern bei der Oxydation verschiedene 
Pigmente. Es ist wohl moglich, dass die bei der enzymatischen 
Spaltung der Glukoside in den Pflanzen entstehenden einfacheren 
aromatischen Verbindungen direkt als Atmungschromogene 

The peroxydase of Chodat and Bach employed by Palladin 
is prepared from the root of the horse-radish. Methods of 
preparation are given by De Stoecklin^^ and are based upon 
the extraction of the ground root with water or dilute alcohol 
and subsequent precipitation w;ith absolute alcohol. The ferment 
separates out as a white powder, which may be purified by solution 
and reprecipitation. The activity of the ferment can be tested by 
its power to produce purpurogallin when added to pyrogallol 
solution in presence of hydrogen peroxide. 

I have prepared the peroxydase by the method of De Stoecklin 
and have tested its action upon an extract of flowers of Primula 
sinensis. Flowers of a white variety slightly tinged with purple 
were gently heated in water and subsequently pounded and filtered. 
To the colourless extract a little of the peroxydase solution was 
added, together with a few drops of hydrogen peroxide. With 

VOL. XV. PT. 11. 11 

152 Miss Wheldale, On the nature of anthocyanin. 

care the formation of a purple pigment can be detected as the 
oxydase is added, though it rapidly vanishes leaving a brown 
colouration only. The same restoration of the pigment is brought 
about sometimes by the addition to the extract of hydrogen 
peroxide only, in which case evidently some of the Primula 
oxydase is still active. It seems probable that the rapid dis- 
appearance of the restored pigment is due to some unfavourable 
condition of the experiment. 

An attempt to isolate an oxydase from the young flowers 
and buds of coloured varieties of Primula sinensis has resulted 
only in the production of a solution which gave a brownish-red 
colour with pyrogallol in presence of hydrogen peroxide but which 
was without effect upon the colourless extract of Primula itself 

Although no positive result has been obtained with Primula 
oxydase on its own chromogen, further attempts will be made 
to isolate a peroxydase from other genera, such as Antirrhinum, 
Lathyrus, etc., and it is possible that these may be more successful. 

The theories of Palladin and Overton however, taken into 
consideration with results derived from work in genetics and from 
the researches of Perkin, seem to provide evidence sufficiently 
strong to justify the assumption, that anthocyanin is a product 
of ferment oxidation of the glucosides of members of the flavone 
series of colouring matters, or of substances very closely allied 
to these. 

If we regard anthocyanin as the product of oxidation of a 
colourless aromatic chromogen, then the following table of genera 
having man}' varieties, shows several anomalies : — 

In Antirrhinum, Dianthus, Matthiola and Verbena, the 
chromogen gives a brown colouration with iron salts, though 
the reactions with basic lead acetate, with alkalis and with 
acids would indicate that it is of a similar nature to those already 
described. In pink — rose doree — Antirrhinum, red Matthiola, 
scarlet Dianthus and scarlet Verbena, the addition of the reddening 
factor produces no change in the iron-reaction but only the 
ultimate addition of a blueing factor, which then produces a green 
iron-reaction — Antirrhinum, Verbena — or a blue iron-reaction — 
Matthiola. In pink Dianthus, the reddening factor gives a green, 
in other varieties the blueing factor, a blue iron-reaction. 

Most frequently, as in Phlox, Lathyrus, Dianthus and Matthiola 
(exceptions Antirrhinum and Verbena^ as well as in Helianthemum 
and Abutilon, the introduction of a blueing factor appears to be 
connected with the production of aa iron-blueing reaction. 

As regards basic lead acetate, the chromogen in Dianthus 
and Matthiola does not give the usual reaction, so that the 
reds and purples become bluer on addition of this reagent but 
no green colour is produced. 

S p: i^ 
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fl a a 

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tp cu 


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CD 03 




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154 Miss Wheldale, On the nature of anthocyanin. 

All forms of anthocyanin so far considered (except the pinks 
of Phlox, Dianthus, Antirrliinum, the pink and scarlet o^ Verbena 
and the red of Matthiola) have been of the type which may be 
termed purple and purplish-red, that is, though the flower-colours 
may be dissimilar, the extracted solution has a purplish tinge and 
the colouration with alkalis is green. 

The following pink and scarlet colours resemble the red 
varieties of Dianthus and Matthiola in giving a red or bluish-red 
colouration or precipitate with basic lead acetate and a full green 
or some green colour with alkalis : — 
Pink Impatiens sultani (violet)*. 

„ Begonia-Glorie de Lorraine (greenish). 
Berries of Berheris vidgaris (unaffected). 
Red Delphinium cardinale „ 

Scarlet variety of Pentstemon sp. (brownish-red). 
From the above examples it is apparent that a difference 
in the reactions with iron salts and with basic lead acetate is 
frequently associated with the production of an anthocyanin 
differently coloured, i.e. pink or scarlet, from the more frequent 
purplish-red form. 

This difference is even more obvious in the following cases 
of scarlet flowers, with the extract of which both alkalis and basic 
lead acetate give a red, purplish-red or purple colour: — 
Scarlet Impatiens Holstii (reddish)*. 
„ Lobelia cardinalis (unaffected). 
„ Salvia splendens (red). 
„ Phaseolus midtiflorus (unaffected). 
„ Papaver Rhoeas (brown-red). 
„ Anagallis grwndifiora (red). 
„ Alonsoa miniata coccinea (unaffected). 
These colour differences may be regarded as further evidence 
in favour of the suggestion that purple, purplish-red and some 
pink forms of anthocyanin are derived from iron-greening chro- 
mogens. When the latter are absent from the plant the flower 
colour is of a strikingly different shade. 

The significance of the change from a green to a blue iron- 
reaction, which so often accompanies a blueing of the anthocyanin, 
is as yet inexplicable. It is possible that as the oxidation of the 
anthocyanin progresses, less of the chromogen remains and hence 
the green iron-reaction of the latter is hidden by the ii'on-reaction 
of anthocyanin itself. This suggestion, however, hardly fits such 
cases as those in which the chromogen is present in a quantity 
sufficient to produce a green colouration with basic lead acetate 
and with alkalis, though at the same time the iron-reaction is 
blue. Probably examination of a larger number of genera may 
* Denotes colour with iron-salts. 

Miss Wheldale, On the nature of anthocyanin. 155 

throw more light upon this point. In connection with the 
statement, that in genera showing various reds and purples, 
i.e. Phlox, Lathyrus, Dianthus and Matthiola, the ultimate purple 
variety contains an anthocyanin giving a blue iron-reaction, it is 
of interest to mention the fact that this ultimate purple anthocyanin 
can often be differentiated into a redder portion (though not 
identical with the anthocyanin of the reds), soluble in alcohol, and 
a bluer portion insoluble in alcohol, but readily soluble in water. 

All cases have not been thoroughly investigated, but as far 
as they go the results point to the conclusion that the bluer 
portion gives a blue precipitate with basic lead acetate, a blue 
colouration with alkalis, and a blue colour with iron salts. 

The bluer portion predominates in berries of Samhiwus nigra 
and Ligustrum vulgare, which give a blue colour with all the 
above reagents. A more careful investigation was made of the 
berries of Ligustrum. For this purpose the dried berries were 
pounded and extracted with absolute alcohol. The alcohol extract 
contained, in addition to chlorophyll, a crimson colouring matter, 
which may be termed (A). When the alcohol ceased to be 
coloured, the residue was dried again and then treated with water. 
The filtrate was deep purple red and contained the greater part 
of the colouring matter of the berries. The purple-red pigment 
may be termed (B). The reactions of the two portions were 
respectively as follows : 

Basic lead acetate 


Iron salts 


Green precipitate 
Blue „ 

Green colouration 
Blue „ 

Dull green colouration 

This result is comparable to those obtained by the following 
authors : — 

Grafe^^ isolated a colouring matter — Malvenfarbstoff — from 
the flowers of Althaea rosea by precipitation of the extract with 
lead acetate and subsequent decomposition with sulphuretted 
hydrogen. The pigment was separated into two portions differing 
in their solubilities, i.e. : — 

Colouring matter (A) Colouring matter (B) 

Soluble in alcohol Insoluble in alcohol but soluble in water 

C14H16O6 C20H30O13 

The author regards (B) as a di-basic acid; the relationship 
between the two pigments is shown in the following equations : — 

C20H30O13 + H2O = CgHiaOg -I- ChHisOs, 
2ChH,80s - 2H,0 - O, - 2C,Ji,,0,. 

156 Miss Wheldale, On the nature of anthoci/anin. 

From this we see that the pigment insohible in alcohol is an oxi- 
dation product and a glucoside of the pigment sohible in alcohol. 

Heise^-' obtained a pigment — Heidelbeerf'arbstoff — from the 
Bilberry which was differentiated into two portions : — 

Colouriug matter (A) Colouring matter (B) 

Insoluble in cold water, soluble in alcohol Soluble in water and alcohol 

CHH14O7 C20H24O12 

The relationship is shown as : — 

C.3„H,,0,, + H,0 = C,H,A- f C„H,A . 


Gautier" also extracted two pigments from the red leaves 

of the Vine — Verfarbungroth der Rebblatter — and termed them 

respectively : — 

a-ampelochi'oic acid |3-ampelochroic acid 

Insoluble in cold water, 

soluble in hot water Soluble in cold water 

Green precipitate with Green precipitate with 

basic lead acetate basic lead acetate 

Dark green with iron salts Dark violet with iron salts 

CioHieOjo C26H24O15 

The results obtained from Ligustrum, Althaea and Vitis seem 
to point to purple anthocyanin as being sometimes a mixture 
of a red and bluer portion, the former giving a green-, the latter 
a blue-iron reaction. The bluer portion is more soluble in water 
and is generally present in greater quantity; this may explain 
the iron-blueing reaction of some purple forms of anthocyanin. 

The analyses made by Grafe and by Gautier suggest that 
the bluer pigment is more highly oxidised, and the change from 
red to blue anthocyanin may possibly be one of oxidation 
resembling the change which causes the colourless chromogen 
to become red. 

The separation of purple pigments into red and bluer con- 
stituents is most obvious in the anthocyanin of certain allied orders, 
i.e.Amarantaceae, Nyctaginaceae,Phytolaccaceae, and Portulacaceae. 
The pigment of these genera differs in its reactions from the usual 
type of anthocyanin* and is at the same time more readily 
separable into two portions distinguished by means of their 
respective solubilities in alcohol. 

Pigment soluble in both 

alcohol and water Basic lead acetate Alkalis Iron salts 

Amaranthus sp yellow precipitate yellow green 

Mirahilis Jalapa orange-yellow precipitate ,, ,, 

BoiigainviUea glabra ... orange ,, green ,, 

Phytolacca decandra orange-red „ yellow ,, 

Portulaca grandifora orange ,, ,, „ 

* Wheldale 20. 

Miss Wheldale, On the nature of anihocyanin. 157 

Pigment soluble in Basic lead Iron 

water only acetate Alkalis salts 

yellow (purple with ammonia) . . . reddish 

Amaranthxis sp orange-red.. 

Mirabilis Jalapa „ 

Bougainvillea glabra . . . red 

Phytolacca decandra ... orange-red.. 
Portulaca grandiflora ... „ 


There is evidently a tendency for the iron-greening reaction 
to disappear as the pigment becomes more oxidised. 

Collectively the results so far obtained as to the nature of 
' anthocyanin ' may be brought to bear upon the phenomena 
observed in the genetics of flower-colour. In Lathyrus and 
Matthiola (Bateson, Saundees and Punnett*) red colour is 
produced by the meeting of two factors G and R, of which G 
has been regarded by the authors as possibly representing a 
chromogen, and R the presence of an enzyme acting upon this 
chromogen with the production of red pigment. If either the 
chromogen or the enzyme be absent, then the plant has lost 
the power of producing red pigment and constitutes an albino. 
Moreover an additional factor B can be carried by the albino and 
B CO- existing with G and R can produce a blueing of the red 
pigment. It seems possible that B may again be an enzyme 
acting upon the red pigment to produce a bluer oxidation product 
as we have seen in Althaea; in which, according to Grafe, there 
are two pigments, one the oxidation product of the other. 

In Antirrhinum the albino (as regards anthocyanin) carrying 
G, the chromogen, is distinguishable to the eye as the ivory-white. 
In the true albino no chromogen is present and no aromatic 
compound can be detected, but since the mating of an ivory-white 
with an albino carrying R produces a magenta cross-bred, the 
true albino probably carries the oxidising enzyme. 

In the yellow variety of Antirrhinum a similar yellow aromatic 
substance is present as a derivative of that in the ivory ; the 
oxidation process in this case gives crimson as a result either 
of the production of a different pigment or of red colouration 
in the presence of unaltered yellow chromogen. 

In Lathyrus and Matthiola, among the offspring produced 
by the selfing of an individual heterozygous in G, R and in 
the white plastid factor which is epistatic to cream, we find the 
proportion of anthocyanic, i.e. purple and red, to non-anthocyanic, 
i.e. white and cream, is as 9 : 7. Moreover among the non- 
anthocyanic, the proportion of whites and creams carrying G 
to those carrying i2 is as 1 : 1. 

Similarly in Antirrhinum, among the offspring from the 
selfing of an individual heterozygous in the yellow chromogen 

* Eeports to the Evolution Committee of the Eoyal Society, i — iv. 

158 Miss Wheldale, On the nature of anthocyanin. 

foctor, in the factor modifying this to ivory and in R, the 
reddening factor, we find the proportion of anthocyanic, i.e. 
magenta and crimson individuals, to the non-anthocyanic, i.e. 
ivory, yellow and white, is again as 9:7. 

Of the non-anthocyanic, the proportion of those carrying G, 
i.e. ivories and yellows, to those carrying R, i.e. true albinos, 
is again as 1:1. 

Through the kindness of Professor Bateson and Mr R. P. Gregory, 
who have been working for some time upon the inheritance of 
fiower-colour in Primula sinensis, I have lately been able to 
examine a number of varieties of this genus. The flowers of 
white varieties contain, as stated on p. 151, achromogen apparently 
of the nature of a flavone. Capability to produce red pigment — 
anthocyanin — is probably due to the presence of an oxydase in the 
plant ; hence a white variety has either lost the power to produce 
the oxydase or contains a positive fjictor — an inhibitor or re- 
ductase — which prevents the formation of the pigment. 

It is possible, on the one hand, that the loss of the oxydase 
gives rise to certain white-flowered varieties with green stems. 
These varieties are known as 'recessive whites'; mated with a 
full-coloured variety, such as deep crimson or magenta, they give 
a full-coloured F^. On the other hand, the presence of an in- 
hibitor in th.e jioiuer only (as suggested by Bateson and Gregory), 
may be the explanation of the existence of certain white-flowered 
varieties having red stems; these varieties are termed 'dominant 
whites' and mated with a full-coloured variety give an F^^ which is 
only tinted. 

When anthocyanin is present, two series of varieties are 
distinguishable, a magenta series and a crimson series, the former 
being epistatic to the latter. As previously stated, the same two 
series, magenta and crimson, occur in Antirrhinum and are probably 
due to the action of an oxydase on the pale yellow flavone of the 
ivory and the deep yellow flavone (xantheiu) of the yellow varieties 
respectively. In Primula no yellow (xanthe'ic) variety arises from 
the crimson but loss of oxydase from crimson and from magenta 
gives whites indistinguishable to the eye, though those thrown 
by magenta contain of course, the magenta factor. 

I have examined the magenta and crimson pigments and also 
the whites derived from each series. Whites from magenta appear 
to carry a chromogen giving a more intense yellow with alkalis 
than those from crimson ; hence magentas give, on the whole, 
a green colour with alkali, due to the blueing of the anthocyanin 
and the yellowing of the unaltered chromogen. The crimsons 
give a bluer colour with alkali due to the far slighter yellowing 
of the unaltered chromogen. The action of iron salts on the 
crimson pigment resultg in a brown, on the magenta in a green 

Miss Wheldale, On the nature of anihocyanin. 159 

colouration. It is probable that magenta and crimson are different 
pigments arising from the action of the same oxydase upon 
different chromogens. 

Hence we see that in Antirrhinum three non-anthocyanic 
varieties exist. Ivory is a 'white' carrying the chromogen giving 
rise to magenta; yellow is a ' white ' carrying the chromogen giving 
rise to crimson in oxidation and the true albino contains no 
chromogen but probably only the oxydase. 

There is some resemblance between Antirrhinum and Primula 
in that one can detect in the latter two kinds of whites carrying 
chromogens giving rise to magenta and crimson respectively but 
the albino containing no chromogen has so far not been identified 
in Primula and may not exist. 

There is moreover a further resemblance as regards the blueing 
factor; in both Antirrhinum and Primula the crimsons and 
magentas are of the purplish-red form of anthocyanin. When the 
blueing factor is absent, varieties arise containing red anthocyanin*. 
In Antirrhinum these are the 'rose doree' (from magenta) and 
'bronze' (from crimson). Similarly in Primula, loss of the blueing 
factor gives rise to 'pink' (from magenta) and 'orange king' (from 

It is conceivable that the green-stemmed variety of Primula 
may represent, in particular so to speak, a class of plants in general 
which do not contain the requisite oxydase and hence can never 
produce red pigment. Galanthus nivalis, Narcissus poeticus, 
Gucurbita Pepo, Helianthus annuus and numerous others would 
be included in this class. 

The red-stemmed white, on the contrary, may be the repre- 
sentative of a class of plants which are anthocyanic but in the 
flowers of which an inhibitor is present. Such plants have white 
or nearly white flowers, though the stems and foliage may contain 
more or less anthocyanin. Some marked examples of this class 
would be Oxalis acetosella, Geranium Robertianum var. album, 
white cultivated Cyclamen persicum, Crataegus oxyacantha, Rosa 
arvensis, Nymphaea alba, Angelica Sylvestris, and many other 

Loss of the inhibiting factor from this latter class would give 
rise to a fully coloured variety from the white-flowered type, the 
exact converse of the origin of a true albino from a coloured type. 
Such cases are rather rare. The most striking examples are the 
origin under cultivation of the deep red and magenta and of the 
pink varieties from the original white-flowered Cyclamen persicum 
which has red stems and leaves. The origin of the tinted Primula 
acaulis from the wild type which has anthocyanin in its petioles 
and leaf-stalks only. 

* Wheldale 20. 

160 Miss Wheldale, On the nature of anthocyanin. 

If the cultivated red varieties of Helianihemum vulgare are 
derived from the yellow type, this would constitute a further 
example. De Vries* quotes additional cases, i.e. red varieties of 
Achillea Millefolium, Begonia, semperflorens, Crataegus oxyacantha, 
Rohinia Pseudacacia, and the red-leaved Beech and Hazel. 

In conclusion I should like to take this opportunity of 
expressing my thanks to Professor Bateson for his valuable advice 
and help in this research. I am also indebted to Mr H. O. Jones 
for suggestions in connection with the chemical portion of the 


1. Chroraogens, pale or deep yellow in colour (in the latter 
case the so-called soluble yellow or xanthe'ic pigments), and of 
the nature of the flavone and xanthone classes of natural colouring 
matters, are widely distributed in plants and are commonly found 
in connection with the pink, purplish-red and purple series of 
'anthocyanic' pigments. 

2. These chromogens exist in the plant probably in com- 
bination with various sugars, i.e., as glucosides. Most of them 
may be regarded as compounds of phloroglucin with protocate- 
chuic acid, hydroxybenzoic acid or sometimes resorcylic acid. 
Occasionally pyrocatechol or some other phenol takes the place 
of phloroglucin. 

3. Overton's work on 'anthocyanin' from the point of view 
of nutrition, also points to the conclusion that this pigment is 
a glucoside compound of a tannic acid. 

4. On the evidence of the recent work of Palladin in 
connection with plant respiration, chromogens of an aromatic 
nature are widely distributed and are able to produce red and 
purple pigments when acted upon by the peroxydase of Chodat 
and Bach in the presence of available oxygen. Hence it is 
highly probable that the bodies mentioned above may constitute 
these chromogens. 

5. Evidence from cross-breeding in Antirrhinum goes to 
prove that for the production of the 'anthocyanin' of the type, 
two bodies are essential, i.e., an aromatic chromogen of the 
flavone series and a reddening factor, in all probability an 
oxidising ferment. 

* Species and Varieties, their Origin by Mutation. 

Miss Wheldale, On the nature of anthocyanin. 161 

6. Hence we may state that successive oxidation stages of 
an aromatic chromogen probably give rise to the colour series, 
pink, purplish-red, and purple of the more commonly occuiTing 
form of 'anthocyanin.' 

7. An albino results either from the loss of the fundamental 
chromogen or from the loss of the reddening enzyme from the 
plant. The blueing enzymes depend for their manifestation on 
the presence of both the first two factors. 

8. In Antirrhinum and Phlox the albino carrying G, the 
chromogen, is ivory-white in colour and is distinguishable from 
the dead-white albino carrying R, the enzyme, not only chemically 
but also in appearance. In Lathyrus and Matthiola no difference 
in appearance can be detected between the albino carrying C and 
the albino carrying R ; in the two latter genera a thorough chemical 
examination of the albinos has yet to be made. 

9. The less commonly occurring scarlet 'anthocyanin' usually 
gives no iron reaction; hence the difference in colour is probably 
connected with a difference in constitution. 

10. The later oxidation stages producing purple 'anthocyanin ' 
are frequently accompanied b}'^ a change from an iron-greening to 
an iron-blueing reaction. It is doubtful whether this is due to 
total oxidation and disappearance of the iron-greening chromogen 
or to a specific reaction of the 'anthocyanin' itself with iron salts. 


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Mr Kleeman, The nature of the ionisation, etc, 169 

The nature of the ionisation produced in a gas by 7 rays. 
By R D. Kleeman, B.A., D.Sc, Emmanuel College, Cambridge. 
(Communicated by Professor Sir J. J. Thomson, F.R.S.) 

[Bead 8 March 1909.] 

The ionisation in a chamber placed in the path of y rays may 
consist of three parts. One part may consist of ions ejected by 
the 7 rays from the gas molecules with a velocity which is so 
small that they are unable to produce any further ions themselves. 
One of the other parts must consist of ions made by the cathode 
i-ays from the walls of the chamber, and the third part of ions 
made by the cathode rays of high velocity ejected from the gas 
molecules. The first of these parts is proportional to the mass 
of the gas and therefore proportional to the pressure, and this is 
also true for the second part since the ionisation of a gas by /8 
rays has been shown to be proportional to the pressure. Since 
the number of electrons ejected from the gas is proportional to 
the pressure, and the number of ions each produces proportional 
to the pressure, the third part is proportional to the square of the 
pressure. The ionisation in the chamber may therefore be expressed 
in the form {(A -\- B)p + Cp^}, where p denotes the pressure. 

Laby and Kaye* have shown that the ionisation in air and 
carbon dioxide is proportional to the pressure over a wide range 
of pressures. The term Cp^ is therefore small within this range. 
Experiments on the variation of the ionisation with pressure will 
not however give any information as to the relative values of 
A and B, since both the ionisation produced by the secondary 
cathode radiation from the walls of the chamber and that due 
to the ejection of slow-moving ions from the molecules of the gas 
by the 7 rays vary as the pressure. Attempts have been made 
to obtain an estimate of the amount of ionisation in a chamber 
which is not due to the radiation from the walls. All these 
estimates depend on some calculations based on certain assump- 
tions, generally involving the absorption, ionisation, etc., of the 
cathode rays produced by the 7 rays. Now the writer has shown 
in a paper in the course of publication f that the 7 rays give rise 
to secondary cathode rays of very different velocities, some of 
these rays have a range in air at atmospheric pressure of the 
order of 2 cm. while some are as penetrating as the penetrating 
/3 rays of radium. It cannot be assumed therefore that the 

* Phil. Mag. p. 879, Dec. 1908. 
t Read before the Royal Society, 



Mr Kleeman, The nature of the ionisation 

absorption of the rays as a whole is the same as the /3 rays of 
uranium, or the penetrating y8 rays of radium. These calculations 
are therefore not satisfactory, they may easily be very considerably 
out. In fact McLennan* deduced that the ionisation in a chamber 
not due to the secondary radiation from the walls is equal to 
about one half of the total ionisation in the chamber, while Wilsonf 
makes it equal to one sixth of the total ionisation. It does not 
therefore appear quite certain that the total ionisation is not due 
entirely to the secondary radiation from the walls. The writer 
therefore made some direct experiments to test this point. 

Several slightly different arrangements were used, each of 
which involved the deflection of the secondary radiation from 
the apparatus by means of a magnetic field. A diagram of the 
apparatus first used is shown in figure 1. ^ is an ionisation 

Fig. 1. 

chamber on a lead block B, 5 cm. thick, the chamber being placed 
symmetrically with respect to an aperture a in the block. 30 
mgrm. of radium were placed at C underneath the aperture. A 
magnet whose poles measured 5 "5 cm. by 5 '5 cm., was placed so 
that the lines of magnetic force traversed the chamber. Since 
the electrons produced by y rays are ejected in the direction of 

* Phil. Mag. Dec. 1907. 

t Phil. Mag. p. 216, Jan. 1909. 

produced in a gas by <y rays. 


propagation of the rays, there was a diffuse pencil of /3 rays 
projected into the chamber from its lower side. If the ionisation 
is produced by the /3 rays from the walls of the chamber, the 
ionisation ought to be principally due to this beam, and should 
therefore decrease considerably when a strong magnetic field is 
applied. It was found, however, that a magnetic field produces 
little change in the amount of ionisation. Thus in a particular 
case the ionisation in a sheet lead chamber 5 5 cm. high, 5*5 cm. 
broad, and 7'5 cm. long, was 1895 in arbitrary units. When a 
field of over 2000 units was applied, which was sufficient to bend 
the rays having the same velocity as the penetrating /3 rays from 
radium into a circle of radius less than 8 mm., the ionisation 
current decreased to 1645, or about 12 7o- When a chamber 
7 cm. high, 4 cm. long, and 3 cm. broad was used, the current 
changed from 1560 to 1475, when the magnetic field was applied, 
a decrease of about 6 °/^. 

If all the ionisation in the gas was produced by the yS rays 
from the walls of the chambers, the ionisation should obviously 
have decreased to a greater extent in each case, although a part 
of the path of each ray when deflected was still contained by 
the chamber, and consequently produced ionisation. 

Since part of the leak in this experiment was always due 
to the /3 rays from the walls of the ionisation chamber, it was 
thought desirable to carry out the experiment in a somewhat 
different form. Figure 2 gives a diagram of the apparatus used. 

A is a cylindrical ionisation chamber 19 cm. long, and 8 cm. in 
diameter, to which the tube ab 6*5 cm. long and 3'5 cm. in diameter 
was co-axially attached. The chamber was placed so that the 
tube ab was between the poles of an electro-magnet. The end 
a of the tube was closed in one set of experiments by a sheet 
of thin aluminium leaf equivalent in mass to a layer of air "7 cm. 
thick, the end b of the tube being closed with a metal plate c. 

172 Mr Kleeman, Tlie nature of the ionisation 

The end d of the chamber A was closed with a thin sheet of zinc. 
£ is a lead block 3 cm. thick through which a circular hole e was 
drilled about 1 cm. in diameter. The axis of this hole and the 
glass tube C containing 80 mgrm. of radium (which was surrounded 
by sheet lead 2 mm. thick), were placed co-axially with the tube 
ah and the ionisation chamber A. The ionisation in the chamber 
was produced principally in the cone /' by the 7 rays from the 
radium and the secondary /3 rays from the plate c, the secondary 
/3 rays being initially projected in the direction of propagation 
of the 7 rays*. The secondary /3 rays produced in a plate are to 
some extent scattered by the plate, but the larger part of the 
radiation proceeds approximately in the direction of propagation 
of the rays. Thus the writer has shown in the paper above 
mentioned that the pencil of secondary /3 rays emerging from 
a plate placed at one end of an aperture in a thick lead block 
while the radium is placed at the other end, is almost exactly 
of the same form as that obtained by shooting the /3 rays from 
the radium through the aperture. The larger part of the radiation 
from the plate c therefore entered the chamber. 

The measurements were carried out by first placing a lead 
plug into the hole e of the lead block B and measuring the leak 
in the chamber. This gives the leak in the chamber due to 
imperfect screening of the lead block B. The leak was then 
measured with the plug removed. The difference between this 
leak and the former gave the ionisation in the cone / due directly 
to the 7 rays and the secondary rays from the plate c. A magnetic 
field of sufficient strength to bend the ^ rays from c so that they 
did not enter the chamber A, was then applied, and the leak again 
measured. The difference between this leak and the first gave 
the leak in the cone approximately due to the direct action of the 
7 rays. 

Whether the strength of the magnetic field was sufficient 
to bend the ^ rays from the lead plate c so that they did not 
enter the chamber A was tested as follows. The plate c and the 
lead sheeting surrounding the radium was removed so that a pencil 
of fi rays from the radium now penetrated into the chamber. 
When the current used in these experiments was switched on 
to the magnet the ionisation was decreased to about 20 °/^ of its 
original amount, showing that practically all the ^ rays were 
prevented from entering the chamber by the magnetic field. 

Firstly some measurements were made with no aluminium 
leaf placed at a. It was found that using a lead plate at c 
2 mm. thick, the ionisation in the cone / decreased 15 7o. when 
the current Avas switched on to the magnet ; when the plate was 
of aluminium 3 mm. thick, the decrease was 23 7o- 

and Madsen, Trans. Roy. Soc. of S. Australia, Vol. xxxii. Jau. 1908. 

produced in a gas hy 7 rays. 


An aluminium leaf was then placed at a, the ionisation in the 
tube ah being now excluded from the leak. The decrease obtained 
with a lead radiator when the magnetic field was applied was 
23 7o> ^^d 31 °/q with the aluminium radiator. 

The secondary j3 radiation from the thin zinc wall d of the 
ionisation chamber produced by the cone of 7 rays / was much 
smaller than that from the plate c because the zinc wall was much 
thinner than the plate, and also because the returned /S radiation 
from a plate is much smaller* than the radiation which is 
propagated in the same direction as the 7 rays, the difference 
being the greater the thinner the plate. The figures obtained 



Fig. 3. 

show therefore that more than 50 °/^ of the ionisation in the cone 
/ is due to the direct action of the 7 rays on the air. 

Some further measurements were carried out with a slight 
modification of the foregoing experiment. A diagram of the 
modified apparatus is shown in figure 3. A is an ionisation 
chamber lOS cm. long, 10*4 cm. broad, and 7 cm. deep, of which 
the upper and lower sides consisted of thin tightly stretched 

* Trans. Roy. Soc. of S. Australia, 1908, Pt. 1. 

174 Mr Kleemav, The nature of the ionisation 

tissue paper, equivalent in mass to a layer of air 1 cm. thick. 
The chamber was placed on the poles B^ and ^3 of an electro- 
magnet, which Avere resting on a lead block C 5 cm. thick. This 
lead block had an aperture a 3 cm. by 3'2 cm., which was placed 
in a symmetrical position with respect to the poles of the electro- 
magnet and the ionisation chamber. D is the tube containing 
the radium placed at a distance of 10 cm. from the lead block. 
The electrode of the chamber consisted of a wire bent into the 
form of a square so that the principal stream of 7 rays through 
the aperture did not impinge upon it. The ionisation in the 
chamber was, as before, principally due to the direct ionisation 
of the gas by the 7 rays and the secondary /3 rays from the plate 
h placed over the aperture a. The plate h was of aluminium 
4 mm, thick. 

The readings were carried out in exactly the same way as 
in the foregoing experiment. The ionisation in the cone c 
decreased to about 55 °/^ of its original value, when a magnetic 
field of sufficient strength to prevent the /3 rays from the plate 
h entering the chamber was applied. This remaining ionisation 
is almost entirely due to the action of the 7 rays on the air in 
the cone c, the ionisation by the secondary radiation from the 
tissue paper being negligible since the paper is equivalent in mass 
to less than a third of the air in the chamber while the ionisation 
by the penetrating radiation from the air in a chamber of ordinary 
size is negligible. 

The returned cathode radiation from the air outside the 
chamber may for our purpose be neglected in comparison with 
the radiation from the aluminium plate h. For if we assume 
that the air is equivalent to a carbon plate giving the maximum 
amount of radiation placed on top of the chamber, the returned 
radiation is about -^ of the emerging radiation*. In the case 
of air it will be less than that, since it radiates to a larger extent 
sideways than the carbon plate. Now, at least one half of the 
radiation emerging from the aluminium plate h enters the cham- 
ber, and if we take the amount of emergence radiation of a plate 
of carbon and aluminium the same, which is approximately true, 
the returned radiation from the air is less than one-sixth of the 
radiation from the aluminium plate. 

It appears therefore from these experiments that the ionisation 
in a chamber is due in part to the direct action of the 7 rays on 
the gas it contains. And since Laby and Kaye have shown that 
the amount of ionisation produced by the secondary 7 and jS 
radiation from the gas is small, this ionisation consists of slow- 
moving ^ rays ejected by the 7 rays, which have not sufficient 
velocity to produce any further ionisation themselves. 

* Bragg and Madsen, Trans. R. Soc. of South Australia, Vol. xxxii. p. 4, 1908. 

produced in a gas by y rays. 175 

The ratio of this part of the ionisation in a chamber to that 
produced by the radiation from its walls, will depend on the ratio 
of the total inside surface of the walls of the chamber to its 
volume, and other conditions. The numbers obtained in the 
experiments just described suggest, however, that in most cases 
this ratio will probaVjly be greater than one half, or the ionisation 
produced directly by the primary 7 rays is in most cases greater 
than 50°/^ of the total ionisation. 

The connection of this result with other quantities will now 
be considered. 

Eve* has made a determination of the total number of ions 
produced per second by the 7 rays from a gram of radium bromide 
in a volume of air which completely absorbs the rays. He 
measured the ionisation in a cylindrical chamber 51 cm. high 
and 23 cm. in diameter, the chamber being made of sheet 
aluminium '4 mm. thick. Assuming the absorption of the 7 rays 
by air to be the same as an equal mass of aluminium — whose 
coefficient of absorption is known — and knowing the volume of the 
chamber and its distance from the radium, etc., the number of 
ions produced per second by the 7 rays of a gram of radium could 
be calculated. In this way Eve obtained 8*9 x 10^^ for the number 
of ions produced. 

The results obtained in this paper suggest that the ionisation 
in his chamber due to the 8 rays produced directly by the 7 rays, 
was roughly about half of the total ionisation ; or, the number of 
B rays produced per second directly by a gram of radium is equal 
to 4'4 X 10". This number should be as near (if not nearer) to the 
true value of this quantity, as that given by Eve for the total 
number of ions produced by the 7 rays of a gram of radium, in 
which case the penetrating /3 rays from the gas are supposed 
to spend all their energy in ionisation. 

Crowtherf has shown that the amount of ionisation produced 
by the secondary radiation from the molecules of a gas exposed to 
X rays is small in comparison with the total amount of ionisation 
produced, and that the ionisation in a gas is therefore principally 
due to the direct action of the X rays. 

This can be shown to be true also in the case of /3 rays. 
The ionisation of the gas in a chamber exposed to /3 rays may 
be divided into two parts. One part consists of slow-moving ions 
or 8 rays produced directly by the primary /9 rays and the 
secondary /S rays from the walls of the chamber. The other part 
consists of the ionisation produced by the /3 rays of high velocity 
ejected from the molecules of the gas. The first part is propor- 
tional to the pressure, while the second part, from what has gone 

* Fhil. Mag. p. 192, Sep. 1906. 

t Proc. Cavib. Phil. Soc. p. 34, Vol. xv. Pt. 1, 1908. 

176 Mr Kleeman, The nature of the ionisation 

before, is proportional to the square of the pressure. Now, Strutt* 
has shown that the ionisation in a gas by /3 rays is proportional 
to the pressure over a wide range of pressures. The second part 
of the ionisation is therefore small in comparison with the first. 
Thus the /3 rays also produce directly rays which do not themselves 
possess sufficient velocity to make any further ions. 

Thus the ionisation of a gas by 7, /3, or X rays, is a measure 
of the number of 8 rays produced directly by the ionising agent. 

Since these rays are not able to produce any further ions 
themselves they must have a velocity less than 2'7 x 10* cm./sec, 
for at higher velocities, according to Townsend, ions are produced 
by collision. 

The writerf has shown that the 7 rays of radium produce 
cathode rays of very different velocities, the maximum velocity 
being equal to that of the penetrating y8 rays from radium. It 
appears therefore that the 7 rays produce cathode rays ranging in 
velocity from 2'7 x 10* to 2*9 x 10" cm./sec. — the velocity of the 
penetrating /3 rays from radium. In the case of X rays cathode 
rays are produced probably ranging in velocity from 27 x 10* to 
8'3 X 10^ cm./sec, the latter velocity being that obtained by Innes 
for the penetrating cathode rays from a plate exposed to X rays. 

Since the most penetrating cathode rays ejected by X rays 
have a range in air at atmospheric pressure equal to a fraction of 
a mm. only, the rays produced in the gas contained in an ionisation 
chamber are entirely absorbed by the gas. The ionisation in 
a gas by X rays is therefore a measure of the energy converted 
directly into cathode rays. Now, according to Crowther, the 
ionisation produced by the secondary cathode rays which are able 
to produce ions by collision is small in comparison with the 
ionisation produced directly by the X rays. It follows therefore 
that the energy expended in the production of penetrating cathode 
rays is small in comparison with that expended in the production 
of 8 rays. And since the energy of one of the most penetrating 
cathode rays ejected by X rays is about 900 times that of a S ray, 
the number of penetrating cathode rays ejected must be very 
small indeed in comparison with the number of S rays ejected. 

Whether this is also true for the cathode rays ejected by 
7 rays cannot yet be determined since there are not sufficient 
experimental data. The penetrating cathode rays ejected by 
7 rays are not absorbed in a distance of a fraction of a mm. in 
a gas like those ejected by X rays, but are able to cross an 
ionisation chamber without any appreciable absorption. And 
since the ionisation they produce in a chamber is small in 
comparison with the total ionisation, this quantity is, provided 

* Phil. Trans., A, vol. 196, p. 507, 1901. 
+ loc. cit. 

produced in a gas hy 7 rays. 177 

the effect of the secondary radiation from the walls of the 
chamber is eliminated, a measure of the energy from the 7 ray 
beam converted directly into h rays. The energy converted into 
penetrating cathode rays may however be (in the case of 7 rays) 
comparatively large, even if a comparatively small number of 
8 rays are produced, for the energy of one of the most penetrating 
rays is about 2000 times that of a 8 ray. 

The coefficient of absorption of a plate of material placed in 
the path of a beam of 7 rays is a measure of the energy converted 
into energy of 8 rays, penetrating cathode rays, and other forms 
of radiation. The ionisation values for different gases, since they 
are only a measure of the energy converted into energy of 8 rays, 
cannot therefore be compared with the coefficient of absorption 
of materials without any knowledge of the comparative magnitude 
of the energies of these radiations. Some information on the 
subject could be obtained by comparing the coefficients of 
absorption of liquids with the ionisations of their vapours. 

It is not improbable that the ejection of penetrating cathode 
rays by 7 rays and X rays is accompanied by the production of 
secondary 7 and X rays, and it would be interesting therefore, 
when sufficient data are available, to compare the relative 
secondary 7 and X radiations from different materials with the 
relative penetrating cathode radiations produced, in order to see 
how much of the secondary 7 and X radiation is accounted for 
in the above way. 


Mr Doncaste7% Note on an abnormal 

Note on an abnormal pair of appendages in Lithohius. By 
L. DoNCASTER, M.A., Lecturer on Zoology, Birmingham University. 

[Beceived 15 March 1909.] 

In dissecting a specimen of the common English Centipede 
{Lithohius forficatus), a student in the Birmingham Zoological 
Laboratory found that it had an extra pair of appendages between 
the poison-claws and the second maxillae. I did not see the 
specimen before the appendages were removed, so cannot say 
exactly how they were attached. The additional pair is repre- 
sented in fig. 1, from a camera-drawing, and fig. 2 represents the 

Fig. 1. 

Fig. 2. 

poison-claws of the same specimen on the same scale. It will be 
seen that the extra appendages are more nearly like poison-claws 
than any other appendages of Lithohius, but differ in several 
important details. They are much smaller, are differently jointed, 
and instead of ending in one sharp tooth on which the poison-duct 
opens, they have at their extremity a triple tooth in which no 
duct is visible. It should be said that they had been soaked in 
potash before they were carefully examined so that a rudimentary 
poison gland and duct might have been present and destroyed. 
Another point of interest concerns the median part of the 

pair of appendages in Lithohius. 179 

appendage. The basal joints of the two sides are more completely 
fused than are the poison-claws, and in the position where the 
latter bear six small processes or teeth on each side, the extra 
appendages bear on each side two larger teeth, which have the 
appearance of being jointed on to the base of the appendage, and 
are not mere processes of it as they are in the normal pair. 

The mandibles and both pairs of maxillae appeared to be 
perfectly normal, and behind the normal pair of poison-claws 
there were as usual fifteen pairs of walking legs. 

180 Mr Boulenger, On the migration of the thread-cells, etc. 

On the migration of the thread-cells of Moerisia. (Preliminary 
note.) By C. L. Boulenger, B.A., King's College. 

[Read 22 February 1909.] 

In a recent paper whilst describing the structure of the 
Egyptian medusa Moerisia lyonsi I called attention to the fact 
that large nematocysts were constantly to be found among the 
endoderm cells of the manubrium. Careful examination of a 
larger series of sections has convinced me that these nematocysts 
are in process of migration through the tissues, a phenomenon 
similar to that recently described by Hadzi in hydroids. 

The main thread-cell batteries in Moerisia are those around 
the oral opening and those on the four perradial tentacles. 

The thread-cells of the oral battery develop in the more 
proximal parts of the manubrium and make their way through 
the endoderm and structureless lamella to the ectoderm of the 
mouth region, the movements being effected by the amoeboid 
cnidoblasts of the thread-cells. Similarly, the nematocysts of the 
perradial tentacles are not formed in situ but probably develop 
in the large ocellar bulbs at the bases of the tentacles. 

Mr Ruhemann, Action of Urethane on Esters, etc. 181 

Action of Urethane on Esters of Organic Acids and Mustard 
Oils. By S. Ruhemann, M.A., Gonville and Caius College, and 
J. G. Priestley, M.A. 

[Bead 8 February 1909.] 

The sodium-derivative of ethyl carbamate reacts with ethyl 
phenyl propiolate not by addition, but with formation of ethyl 
phenylpropiolylcarbamate. Similarly the esters of fatty saturated 
acids furnish acid derivatives of ethyl carbamate. 

Phenyl mustard oil reacts with ethyl sodiocarbamate mainly 
according to the equation: 

2C6H5NCS5 + NaNH . CO,Et - dsHioONaS^Na + C^HsO, 

and yields the anhydride of diphenylthiobiuretcarboxylic acid. 
Besides this compound, a small quantity of carboxyethylphenyl- 


is formed. Analogous is the action of ethyl sodiocarbamate on 
other mustard oils. 

182 Dr Fenton and Mr Robinson, Homologiies of furfural. 

Homologues of furfural. By Dr Fenton aud F. Robinson, 

{Read 8 February 1909.] 

New syntheses have been effected by the application of the 
Fried el and Crafts reaction to the halogen derivatives of methyl- 
furfural with various hydrocarbons and the results promise a wide 
field for further investigation. Improvements have been made in 
the mode of formation of the derivatives of methylfurfural and 
evidence is brought forward which appears to necessitate a modi- 
fication in the generally accepted constitutional formula for the 



On a configuration of ticenti/seven hyper-planes in four-dimen3io7ial 

spaces. By Professor W. Burnside 71 

Note on some double fiuorides of sodium. By W. A. R. Wilks. 

(Conmmnicated by Dr Fenton) 76 

An experiment on ionisation with y rays. By L. Yegard. (Com- 

nnmicated by Professor Sir J. J. Thomson) . . . . 78 
The absorption spectra of solid tetramethylpicene and of its solutions. 

By J. E. Purvis and Miss A. Homer 82 

The absorption spectra of concentrated and diluted solutions of chlorophyll. 

By J. E. Purvis. ' (Plates I— III) 85 

The absorption spectrct of mesitylene and tricMoromesitylcnc. By J. E. 

Purvis 89 

On a so-called '■^ sexvxd" method of forming spores in Bacteria. By 

C. C. DOBELL 91 

On the alleged iurliwnce of lecithin upon the determination of sex in 

rabbits. By E. C. PuNNETT 92 

A coloured thio-o.valate. By H. 0. Jones and H. S. Tasker . . 94 
Obscrrations on the changes in. the Common Shore-crab caused by 

Sacculina. By F. A. Potts. (One fig. in Text) ... 96 

On the secondary R&ntgen radiation from air and ethyl bromide. By 

J. A. Crowther. (One tig. iu Text) 101 

^4 string electrometer. By T. H. Laby. (Five figs, in Text) . . 106 

Interference fringes with feeble light. By G. I. Taylor. (Communicated 

by Professor Sir J. J. Thomson) .114 

On the parametric representation of the coordinates of points on a cubic 

surface in space of four dimensions. By H. W. Richmond . , 116 
The study of discontinuous phenomena. By Normax Campbell . . 117 
On the nature of anthocyanin. By Miss M. Wheldale. (Communi- 
cated by Professor Bateson) 137 

The nature of the ionisation produced in a gas by y rays. By R. D. 

Ivleeman. (Communicated by Professor Sir J. J. Thomson.) 

(Tln-ee figs, in Text) . . .169 

jyotc on an abnormcd- pair of appendages in Lithobius. By T,. DON- 

c ASTER. (Two figs, in Text) .178 

On the migration of the theeacl-rells of Mwrisia. (Preliminary note.) 

By C. L. BouLENGER 180 

Action of Urethane on Esters of Organic Acids and JIustard Oils. By 

S. Ruhemaxx and J. G. Priestley 181 

Homologues of furfural. By Dr Fenton and F. Robinson . . . 182 




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dtamkitrge ^Ijil0S0p]^kaI Snmtg* 

So7ne fatigue effects of the cathode in a discharge tube. By 
R. Whiddington, B.A., Hutchinson Research Student of St John's 
College. (Communicated by Professor Sir J. J. Thomson.) 

[Read 17 May 1909.] 

Skinner's* experiments on the vacuum tube discharge seem to 
suggest that charged hydrogen atoms emitted from the cathode 
play a considerable part in the carriage of the current. 

Chrisler-f- has studied experimentally the effect of absorbed 
gases on the photoelectric activity of metals, coming to the 
conclusion that hydrogen again plays a large part in the photo- 
electric current. 

The pi'esent note describes the results of some simple experi- 
ments designed to show what influence the gases occluded in the 
cathode have on the emitted cathode rays. 

The method employed is qualitative and hardly capable of 
quantitative application. It consists of comparing the behaviour 
of a cathode, previously treated in various ways, with an exactly 
similar, and similarly situated untreated standard electrode, in 
the same tube. By this means the complicating influence of 
pressure changes was eliminated, for the change over from one 
cathode to the other was instantaneous leaving no time for a 
change in pressure. 

If the looked-for effect has any existence it is reasonable to 
suppose that it might be greatest in the case of a charcoal 
cathode. For carbon can be made to absorb vast volumes of 
many gases. 

* Fhys. Rev. Vol. xxi. 1905. 
t Phys. Rev. Vol. xxvn. 1908. 

VOL. XV. PT. III. 13 

184 Mr Whiddington, Some fatigue effects 

The first experiments accordingly were made with cocoanut 
charcoal electrodes. 

Two circular carbon electrodes of equal thickness and about 
two centimetres in diameter were mounted symmetrically and 
parallel in a vertical straight tube only slightly larger, so as to 
face each other at a distance of about 30 centimetres. A sub- 
sidiary aluminium electrode was fused in, in a side tube midway 
between the two cathodes. Further, each carbon electrode was 
arranged so as to be at the geometrical centre of a concave alu- 
minium electrode, which, when run as cathode, bombarded its 
attendant carbon electrode with an intensely heating beam of 
cathode rays. 

The upper electrode was taken as the standard. The lower 
electrode was heated up by the convergent beam of rays from its 
concave cathode, the resulting spot of incandescence being moved 
about by means of a bar magnet. After four or five hours' 
continuous heating and pumping the carbon ceased to give off 
gas, indicated by the width of the Crookes' dark space remaining 

The spectroscope showed the emitted gas to be mainly oxides 
of carbon with a perceptible trace of hydrogen. 

The tube now contained an upper electrode full of gas, and a 
lower one free of gas. The two electrodes were then connected 
direct to the secondary of an induction coil (giving a 6 in. spark). 
On making alternately the upper and lower carbon electrodes, 
cathode, no difference in the character of the discharge could be 
detected. The cathode ray emission as roughly indicated by the 
green glass phosphorescence was the same and the Crookes' dark 
space was in both cases of* the same width. 

Now, on running the lower carbon as cathode for 10 minutes, 
the subsidiary side electrode being anode, a further small quantity 
of gas was given off indicated by the shrinking in of the dark 
space. As before the gas appeared to be oxides of carbon and 

A comparison of this now further depleted lower carbon with 
the standard showed a distinct alteration in properties. The 
green glass phosphorescence was very much less brilliant and the 
Crookes' dark space narrower and more sharply defined. After 
20 minutes running as cathode, this fatigue effect, as it may be 
called, became more marked ; but after half an hour the cathode 
seemed to get into a constant state. The state of affairs can be 
summed up in few words by saying that the upper standard 
cathode behaved as though the tube were hard, the lower one as 
though the tube were soft, yet the gas pressure was the same in 
either case. 

The fact that the boundary of the Crookes' dark space 

of the cathode in a discharge tube. 185 

becomes more sharply defined with time of running, seems to 
suggest that the cathode rays emitted by the fresh cathode have 
various velocities, but that as the running is continued, the faster 
and more penetrating rays cease to be emitted in any quantity, 
until at last when the cathode is quite fatigued the rays are very 

Having reduced the lower carbon to this fatigued state 
attempts were made to restore it to an equality with the standard. 
To this end it was caused to absorb hydrogen, air, carbon dioxide 
[and helium] by cooling in liquid air and admitting the gas. 

No appreciable return to equality with the standard could be 

It should be mentioned that during the absorbing process the 
upper standard carbon electrode was kept hot to prevent any 
absorption taking place there. This meant that both oxides of 
carbon were being absorbed by the lower electrode during the 
admission of carbon dioxide, for carbon monoxide would be con- 
tinuously produced by the union of the incandescent upper carbon 
with the surrounding carbon dioxide. 

Platinum electrodes were next tried, the heating in this case 
being produced by the passage of an electric current. No certain 
results could be obtained owing to the erratic behaviour of the 
platinum after heating. The only point that could definitely be 
established was that, as in the case of the carbon, running as 
cathode could liberate gas which mere heating could not. 

Aluminium electrodes were next tried but without any heating 
arrangement. The same fatigue effect though rather less marked 
than with carbon was observed. Again it was found impossible 
to restore the cathode to the original (standard) state by causing 
the metal to absorb various gases. The method of causing gas 
absorption in this case was to heat up the metal to about 400° C. 
in a glass tube containing the gas required and then allowing it 
to cool. In this way some little of the gas was always absorbed. 
A considerable volume of hydrogen could be introduced into the 
body of the metal in quite a different way. The cathode was made 
one of the electrodes in an electrolytic cell containing dilute 
sulphuric acid and the current passed so as to deposit hydrogen 
against the aluminium. Although this caused considerable 
absorption of hydrogen yet the fatigued metal showed no return 
to the standard state. 

It is well known that the green phosphorescence excited on 
glass by cathode rays falls off in intensity as the bombardment is 

This effect was eliminated by using a horizontal discharge 
tube with the electrodes as before facing each other at either end, 
in the centre of which was suspended a Willemite screen carrying 


186 Mr Whiddington, Some fatigue effects 

a little magnet so that the screen could be rotated by an external 
magnetic control. The screen was midway between the two 
electrodes. When both electrodes were fresh the phosphorescence 
of the screen was independent of the cathode from which it 
received the exciting cathode rays. When, however, one of the 
electrodes was run as cathode for some time, the Willemite glowed 
much more vividly when it was responding to rays from the 
fresh cathode, the dark space being a centimetre or so in width 
and the distance of the screen about 5 cms. 

This fact lends support to the view that at any rate some of 
the rays emitted from a fresh cathode are faster and therefore 
more penetrating than those emitted from a run cathode. 

The surface of the aluminium used in the above (and future) 
experiments was always polished with the finest emery powder so 
as to be sure of always having a constant surface. 

It was thought that the observed effects might be merely due 
to surface influences. This was proved to be not so, by filing off 
about "2 mms. of the metallic surface and repolishing. The run 
cathode so treated appeared to be still as fatigued as ever. 

A fatigued cathode also shows no very marked signs of recovery 
if left to itself In one particular case a tube was left at atmo- 
spheric pressure for over three months and at the end of that time 
the fatigue effect was still as obvious as it had been immediately 
after the running period. 

At first, running the fatigued cathode as anode did not appear 
to have any effect, but using a very small induction coil (giving 
5 mm. spark) to produce the discharge, an effect was observed 
when the pressure was between certain limits. When the fatigued 
cathode which had been run as anode was made cathode again, 
there was a sudden burst, so to speak, of phosphorescence when 
the discharge first passed. This sudden brilliance however was 
only momentary, lasting but a small fraction of a second. This 
transient recovery did not seem to depend on the length of time 
the electrode was run as anode ; making it anode momentarily 
produced as much effect as running for quite a long time. The 
effect was most marked in hydrogen but could be got in other 
gases as well. 

Chrisler in the paper cited quotes figures showing that the 
photoelectric current for metals increases enormously if the elec- 
trode is run momentarily as anode in hydrogen. This falls into 
line with the cathode effect described above, but his further 
observation that running as anode in gases other than hydrogen 
actually diminished the photoelectric effect finds no counterpart 
in these experiments. 

It was thought that the volume of metal forming the cathode 
might influence the time taken to produce the fatigue effect. 
Experiments on this point gave no definite results. 

of the cathode in a discharge tube. 187 

The direct results of these experiments are : 

(i) That an electrode contains gas which cannot be driven 
off by an ordinary heating but which is easily evolved when the 
electrode is run as a cathode. 

(ii) That an electrode after running as cathode for some 
time emits more slowly moving and more homogeneous cathode 
rays than it does when fresh. 

(iii) That it is not possible to restore a "fatigued" cathode to 
its original state by causing it to absorb hydrogen, oxygen, nitrogen, 
carbon dioxide, carbon monoxide or helium. 

It was thought that measurements of the cathode fall of 
potential might throw some light on (ii). 

The cathode fall was measured only in the case of aluminium 
cathodes in air. 

A platinum exploring point was used in conjunction with an 
Ayrtou- Mather electrostatic voltmeter. 

The instrument always took from half to three-quarters of a 
minute to reach its final reading owing both to the smallness of 
the collecting point and the large capacity of the electrometer 
quadrants. The arrangement could therefore not be used to 
measure rapid variations in the cathode fall. 

In most cases the cathode fall started from a low value, rising 
rapidly in about three minutes to a maximum and then gradually 
falling to a final steady state. No value can be attached to the 
first rapid rise to a maximum as very often the time taken was 
comparable with the time of lag of the instrument. The value of 
the maximum recorded by the electrometer was very variable with 
different cathodes, even when they were cut out of the same sheet 
of metal. The limits of variation were between 280 and 400 
volts. In only one case was the upper limit reached, usually 
300 volts was about the value. The final value to which all 
cathodes converged was 265 volts and the time taken was of the 
magnitude of 10 minutes. 

Thus the cathode fall for a new aluminium cathode is rather 
greater than for one which has been run some time, the difference 
usually being about 20 °j^ but sometimes being as much as 60 " j^. 

This is what the qualitative experiments might have led 
one to expect ; for a new cathode has a wider dark space than 
a run one. 

The effect of absorbed gases was tried but with negative 

Running the cathode as anode also produced no change that 
could be detected in the cathode fall. This again is what the 
previously described experiment might be taken as predicting ; 
for the effect could only be a momentary one and could not be 

188 Mr Whiddington, Some fatigue effects of the cathode, etc. 

detected owing to the great time lag of the instrument. No 
collecting point device could be expected to indicate changes in 
potential so rapid as this. 

Some quite thin aluminium plate '01 cm. thick was tried in 
the cathode fall tube. It was found that the cathode fall rose 
almost immediately to the final value 265 volts instead of starting 
from a high value and then slowly diminishing with time. 

This observation suggested that the time taken for a cathode 
to give its final value for the cathode fall might depend on the 
volume of the cathode, the time being greater, the greater the 
mass of metal involved. 

Such time effects were looked for but could not be quantita- 
tively worked out owing to two main causes, firstly to the fact 
that different cathodes did not start from the same high value of 
the cathode fall although they all reached the same final value, 
and secondly to the fact that even two electiodes of the same 
thickness and size cut out of the same sheet of metal and starting 
from almost the same high value took very different times to reach 
the same final limit. 

In general however it seemed certain that for heavy cathodes 
a considerable time was required to reach a steady state, while 
light cathodes reached it immediately, without any gradual fall. 

This result led at once to the trial of very thin cathodes in 
the ordinary discharge tube. They did not show any fatigue 
effect, the dark space being sharply defined from the commence- 

It is possible that some gas is present in the new metal which 
is expelled by running as a cathode which is responsible for these 
fatigue effects. If the gas is one of those mentioned above it 
certainly cannot be made to enter the material of the cathode in 
the ordinary way. On the other hand it may be one of the rarer 
gases or even an unknown one. 

It is possible that photographic methods using large masses 
of metal for the cathode may reveal this gas. But in these 
experiments the only gases evolved appeared to be oxides of 
carbon and hydrogen. 

I have pleasure in thanking Prof. Sir J. J. Thomson for 
suggesting the work and for his kind interest while it was being 
carried out. 

Mr Whiddington, Note on the electrical behaviour, etc. 189 

Note on the electrical behaviour of fluorescing iodine vapour. 
By R, Whiddington, B.A., Hutchinson Student of St John's 
College. (Communicated by Prof. Sir J. J. Thomson.) 

[^Received 4 August 1909.] 

In view of the fact that no satisfactory theory of fluorescence 
exists, it was thought likely that a study of the electrical be- 
haviour of iodine vapour when fluorescing might give valuable 

The apparatus employed consisted of a wide glass tube into 
which a cylinder of copper gauze slipped tightly. The light 
could be concentrated within the tube through a hole cut in the 

The electrodes were discs of copper placed parallel and at a 
distance of about three centimetres apart. One electrode was 
earthed and connected to the gauze sheath, the other being 
connected to a sensitive Wilson gold leaf electroscope. 

In the first trials ebonite insulation was used, but as the 
iodine — which was liberally sprinkled within the vessel — was 
found to attack it, quartz was substituted in its stead. 

The vessel was connected to a mercury pump and evacuated 
to the limit set by the vapour pressure of the iodine {-^ mm. 

When a beam of arc light was focussed between the electrodes, 
the fluorescence was plainly visible but no trace of ionization 
could be detected even when the applied electric field was almost 
enough to produce a discharge. 

To be quite certain that the ionization chamber and electro- 
scope were in good working order, a test was made with a weak 
sample of radium. Even at this low pressure there was a very 
rapid deflection of the gold leaf 

This experiment conclusively shows that ionization is not 
necessarily an accompaniment of fluorescence. 

190 Mr Sharpe, On the Re/lection of Sound at a Pai-aboloid. 

On the Reflection of Sound at a Pai-aholoid. By the Rev. H. J. 
Sharpe, M.A., late Fellow of S. John's College, Cambridge. 

[Received 22 May 1909.] 

38. In the year 1899 a Paper by the author with the above 
title was published in Vol. X. Part iii, of the Proceedings of the 
Camhridge Philosophical Society. That Paper contained some 
minor and possibly some major Errata, which I should like some 
day to correct, but that is not my object at present. Rather it is 
to make an addition to my former Paper suggested by Arts. 10, 18 
and 23, in which additional results are obtained, shewing a strange 
analogy with the Retiection of a point of Light at plane surfaces. 
Thinking it would be better to make this Paper intelligible by itself, 
I have ventured to repeat, as shortly as possible, some of the early 
part of the Analysis. Wishing also this Paper to be considered 
part of the first, I have made the numbering of the Articles, 
Equations, and figures run on continuously. 

39. Suppose then (fig. 8) LR to be the material parabolic 
Reflector, its focus and OiV the axis of x. The sound motion is 
supposed to be such that it is everywhere symmetrical round the 
axis, and in planes passing through it. 

Let P be any point within the Paraboloid LR. Draw two 
confocal parabolas PU and PY passing through P with as 

focus. Put 0U=%,0V=~ and 0L = \:. It will be found that 

any sound motion within the Paraboloid must satisfy the following 

u + V \ dv' du- dv duj a- df ' 

Mr Sharpe, On the Reflection of Sound at a Paraboloid. 191 

For sound motion F will be of the form 

P sin {Ipat) + Q cos {'^pat), 
where P and Q each satisfy the equation 

u + vX dv^ du^ dv duj ^ 

As in the present Paper we shall only consider stationary 
vibration, either P or Q will always be zero. A particular solution 
of the last equation is P = UV, where U is & function of u only, 
and F of -y only, and 

»!?+'£+ (^''-^>'^=° (««>' 

^2 JT (ITT 

^^ +^ +(^'" +^) ^=^ (97X 

du^ du 

where A is an arbitrary constant, pa/ir is the frequency and a is 

the velocity of sound. It will be found that the condition of 

reflection at the paraboloid LP is that -^ should = when u = l. 

In all that follows it will be found to conduce much to brevity 
to use new independent variables, defined thus 

pu = u', pv = v', pi = r and A/p = A'; 
(96) and (97) then become 

'''^+S7 + (»'-^'>''=« (««)• 

u'yi, + yT^-{u+A')U=Q (99), 

du^ du 

from which p has disappeared and the condition of reflection 

^,=0 whenw' = r (100). 

du ' ' 

We may now drop the dashes, if in all final results we re- 
member to put 

pu for u, pv for v, pi for I, and Ajpi for A. 
By this we come back to the original notation. 

40. We will first take a comparatively simple case. We will 
suppose JL = 0. This case was partly treated in Arts. 10 — 17, but 
more will be added. In this case we get F= Ju('y) and U = J^{a), 
and the condition of reflection is that d U/du = when u = l. 

192 Mr Sharpe, On the Reflection of Sound at a Paraboloid. 

It is known that the equations Jo (u) — and -v- Jo (u) = have 

an infinite number of real roots, so that I has an infinite number 
of values appropriate to the present solution. The same can be 
said of the original pi (Art. 39), and (as we suppose p constant) of 
the latus rectum of the Reflector. It will be interesting to find 
the various points on the axis where the air- velocity is a maximum, 
and especially the position and intensity of the greatest maximum. 
We shall suppose the vibration stationary, then it can be shewn 
(Art. 5) that the air- velocity in the direction OV (fig, 8) at any 

point V on the axis is 2 -r- x time factor, which =2-^ Jo(v) x 

time-factor. We shall, however, for brevity always omit the 
time factor. The position on the axis to the right of where 
the air-velocity is a maximum is determined by the equation 

-Y-„ Jo (v) = 0, which is the same thing as -^ J\ («) = 0. 

Now the zeros and turning points of Ji {x) are given by the 
following Table, where, for simplicity, we have retained only two 
places of decimals. 

When a; = 1-84, 5-33, 8-54, 11'71, 14-86, 18-00, &c. 

Then -^ Jo {x) = — J^(x) = 

-•58, +-34, -'27, +-23, -'20, -h 19, &c., 
and the roots of Jj (x) — are given by 

x = 0, 3-83, 7-01, 10-17, 13-32, &c. 

Looking at fig. 8, if P' be the optical image of P in OR', we 
see that the « and v of P will be equal to the v and u of P' 
respectively, and when A = 0, it will be found (see Art. 5) that 
the sound motion to the left of OR' is the image of the sound motion 
to the right of OR'. It follows that if in fig. 8 we draw the parabola 
L'R' the image of LR', there will be no air-velocity normal to 
L'R'; and L', as tuell as L, will be a point of rest. 

We can now see something as to the nature of the air motion 
and sound intensity, at any rate at points along the axis of the 
reflector LR'. To the right of OR' (see fig. 9) along the axis Ox 
we have an infinite series of points Vi, Vo, Vg, ^4, etc., whose abscissae 
are Ovi=l-84, 0^2=5-33, etc. The ordinates of the wavy curve 
represent the magnitudes and directions of the corresponding 
maximum air-velocities. 

For instance, at Vj the magnitude is -58 to the left, 

Vo^ „ „ -34 „ right, 

Vs „ „ -27 „ left, and so on ; 

''1, f'a, *'3j '"45 etc., are intermediate points of rest. 

Mr Sharpe, On the Reflection of Sound at a Paraboloid. 193 

It will be observed that as we pass from infinity along the axis 
from X towards the maxima air-velocities gradually increase in 
intensity till at Vi we have the greatest maximum. 

On the left of OR' we have a state of air- velocity at Ui, u^, u^, etc., 
P\, P-2, p3, etc., exactly the image, in the line OR', of that which 
exists on the right of OR'. Of course on the right of Vi,V2,V3, etc., 
are real foci of reflection. But on the left of (as the figure is 
drawn) only Ui and U2 are real foci, all the rest U3, u^, etc., are 
virtual foci of reflection. And here it must be noted that the 
point r^ in fig. 9 is supposed to be identical with the point L' in 
fig. 8. The points L and L' being points of no air-velocity must 
be made identical with some of the points ri, r^, etc., and p^, p^, etc., 

Fig. 9. 

in fig. 9 — taken in pairs as r^pi, r2p2, ^sps, etc. As we have 
chosen the size of the Reflector so that L' coincides with r^ (fig. 9) 
we shall have I (or. Art. 39, going back to the original notation) 
pi = 7"01. Suppose ^ to be 8 inches (the size of a portable Sound 
Reflector I actually made). Then |)=1051, a high note just 
within the range of a piano. 

Suppose (fig. 9) we had made L' to coincide with r^ (instead 
of Ta) we should have gotjjl = 3*83, and then p would be 5*74. We 
thus see that as we experiment with higher and higher notes, 
more and more points of maximum velocity are crowded into the 
space LL' (see fig. 8) that is in the neighbourhood of the focus 0. 
It must, however, be noticed that in this case where A = 0, which 
we have been considering, is always a point of rest. 

194 Mr Sharpe, On the Reflection of Sound at a Paraboloid. 

41. We will next suppose A finite. We have now to use the 
equations (98) and (99) — but we will drop the dashes and no 
mistake will arise if we are careful to remember the remark at the 
end of Art. 39. 

In (98) and (99) A is one of the roots of the equation in A 

dU/du = 0, when u = l (100). 

Suppose, if possible, A^ and A^ to be two different roots of this 
last equation, and when A = Ay, A2 respectively, let U become 
Ui, U2 respectively. Then 

d^Uy dU, , , ^ rr ^ 

d^Uo dU» , . . T~T 

It is easy to shew that 

'^^^'^^ +{A,-A,)UJJ, = 0. 


^ du ^ du) 

Integrate this with regard to u between the limits and I, 
when we get 

^ UyU,du = (101). 

This shews that the equation (100) considered as an equation in A 
has all its roots real, for otherwise, if Ai and Ao were two conjugate 
unreal roots, (101) could not be satisfied. 


42. We will next suppose that in (99) u is much larger than 
A, then it is evident that, in the neighbourhood of points which 
satisfy this condition, U does not differ much from Jo(u), and 
the curve whose ordinates give dU/dii is a wavy or periodic curve 
Avhich cuts the axis. This is corroborated by Art. 23, where it is 
shewn that if w > ^ we have approximately 

U=—cos(u + ^A \ogu + a) (102), 


where B and a are constant functions of A. 

[N.B. In Art. 23 we have V, v and —A, but it will be found 
that exactly similar reasoning may be applied to the case IT, 
u and + J..] 

We will next suppose that v is much larger than A, then we 
can shew in like manner that, near points which satisfy this con- 
dition, the curve whose ordinates give dV/dv is a wavy curve 

Mr Sharpe, On the Reflection of Sound at a Paraboloid. 195 

which cuts the axis, also when v>A we have approximately from 
Art. 23 

V=-^cos(v-^A\ogv + a') (103), 

where B' and a' are constant functions of A. 

43. We will next suppose that in (99) u is much smaller than 
A. Then divide each side of (99) by A and put Au = z. We 
then get approximately (see Art. 19 of this Paper), if z is large, 

• TT J- /n ix COS {2 (Au)i - lir] 

This shews that in the neighbourhood of points which satisfy 
the condition u\A small {A being large) the curve whose ordinates 
give the velocity dUjdu is a wavy curve which cuts the axis. 

We will next suppose that in (98) v is much smaller than A. 
Proceed as before. Divide by A and put Av = z. We shall then 
get approximately (see Art. 20 of this Paper) 

F=^=l+^+^ + ^ + etc. = /„{2(-^)4l. 

It is evident from this, that in the neighbourhood of points 
satisfying the condition v <A {A being large) no positive value of 
V can satisfy the condition oidVjdv being a maximum or minimum, 
and that therefore near such points the curve, whose ordinates 
give dV/dv, is either not a wavy curve at all, or if it is a wavy 
curve, that it does not cut the axis. This kind of curve is shewn 
by the wavy line in fig. 10. Or it is possible, but not likely, that 
between and A the velocities might uniformly increase or 
uniformly diminish without there being maxima or minima. 
Perhaps we might be allowed to speak of this kind of curve as an 
exponential curve. All this is further corroborated by the fact that 
when z is large the approximate value of V takes an exponential 
form (see Art. 20) 

V=~ r (105). 

44. We have now examined the shape of the air-velocity 
curve in the neighbourhood of four classes of points defined thus 

u> A, u<A, v>A, v<A. 

It remains to examine the same near four other classes of points 
defined thus 

u does not differ much from A in excess or defect, 

190 Mr Sharjic, On the BcfJccHoii of SoiDid at a Paraboloid. 

Wo shall take the two lj\st cases tii-st. In (98) put v = A/x and 
suppose both v and A large, and /t nearly = 1. 

And tirst we shall suppose fi<l, equation (98) then becomes 

d'V dV 

^,^,^^u:-'''^''-''^' ^''''- 

With the above suppositions, a solution (68) is given of this 
equation in Art. 26. [It must, however, be admitted that (68) 
fails if jLi be too near 1. For this ea^e and for the ciise of yu, 
being actually = 1 another solution nnist be sought.] The solution 
(68), however, answei"s very well if say ^ is near h. It will be 
further observed that the solution (68) is of an exponential 
character, so it seems to follow by reasoning similar to that used 
before that (for points for which /.kI, but v and A both large) 
the air-velocity curve is exponential. It is important to observe 
that this result agrees very well with the latter part of Art. -iS. 

45. Next, with the above suppositions, we shall suppose ^ > 1. 
In this case it is better to write the equation for V thus 

d'V dV 

A solution (70) of this equation is given in xlrt. 27. 

[As before, we must admit that this solution fails when /x is 
very near 1 or actually =1. but it answers very well if yti is near 
or = L] It will be further observed that the solution (70) is of a 
trigonometrical or periodic character, so it seems to follow as 
before that (for points for which /u,> 1, but v and A both large) the 
air-velocity curve is wavy and cuts the axis. Again it will be 
observed that this agrees very well with the latter part of Ai-t. 42. 

46. According to the beginning of Art. 44 it would now be 
our duty to examine the value of i" when u does not ditier much 
from A in excess or defect. In (99) put u = A/ll, and suppose u 
and A both large, then (99) becomes 

''!?'+!?;: +-^'^'^^ +'''=» (1"^'^- 

As fi is supposed nearly = 1 this equation does not ditier much 

d'U , dU , , ,,„ , 
'^ d/x- dfi 
Put '2A-/X = i: Then 

d'U dU „ , 
dv- dj' 

Mr Sharpe, On the Reflection of Sound at a Paraboloid. 197 

Then U^JA^vh^JA^^^A' ^' 

As J. is large and fi about 1, we get nearly 


This shews that the air-velocity curve near the points defined 
as above is wavy and cuts the axis. It seems probable that this 
solution will take the same form whether /x differs from 1 in 
excess or defect. 

47. I will now give a figure (fig. 10) which will illustrate at 
one view the chief results arrived at in Arts. 42 to 46. The 
figure is of course not drawn to scale. The Numbers 42 (1) etc. 
refer to Art. 42, First Part, etc. The little dots together 
near a large point on the axis mean that the air-velocity curve 
near the point is wavy, like that in fig, 9, and cuts the axis. 

U HJH m\m — \ — I 1-^^ — f-wKi 1 H^w 

H I t " i . , 

42 L. A 43 O 43 44 A' 45 L' 42 

(1> 46 (1) (2) (2) 

Fig. 10. 

In this figure LAO A' is the axis of the Reflector of which is 
the focus and L the vertex. OA is measured to the left o( = A 
and OA' to the right = A. One curious result is that at all points 
between and A' on the right of the velocity curve is 
" exponential." 

198 Mr Bobh, Discmsion of a difference equation relating to 

DiscKsi^ion of a difference equation relating to the tension of 
overhead wires supported hy equidistant poles. By A, A. RoBB, 
M.A., St John's College. 

[Beceived 22 May 1909.] 

Section I. On the Form of the Solution. 

When overhead wires are suspended from poles for electrical 
purposes, certain precautions must be taken in adjusting the 
tensions, since otherwise the snapping of the wire may lead 
to the breakage of a large number of poles. 

The mathematical problem thence arising has already been con- 
sidered by several writers and among others b}' Messrs Hawthorne 
and Morton in the Philosophical Maga:ine, Vols. xi. and xii., 1906. 

Their result is somewhat vitiated through taking the quantity 
denoted by '"/'" a^ a constant : whereas it generally varies through a 
wide range (Vol. XI., p. Go-iV 

The attention of the writer was drawn to the problem by 
Mr W. H. Logeman who has himself investigated it by a gfaphi- 
eal method which is hovvever quite different from the following. 

In practice the wire is stretched between "anchor poles" which 
are often long distances apart and may be regarded as rigid; while 
between these it is supported by ordinary poles which in normal 
circumstances are not subject to transverse stress. When a break 
occurs in the wire, the ordinary poles are subject to tbrces tending 
to detlect them and the detiecting force on a pole is equal to the 
difference between the horizontal components of the tensions in 
the two adjoining sections of wire. 

If these forces lie within the limits of safety the deflections of 
the poles will be proportional to them and we may assume a con- 
stant of proportionality H, such that the horizontal displacement 
of the point of attachment of the wire = JT (detiecting force). 

Let jfj, To, Ts, ... be the horizontal tensions in successive 
sections of the wire counting from the break and let L be the 
common distance between successive poles. 

If X.„ be the horizontal displacement of the top of the nth pole 
counting from the break, we have 

Thus \„+, - X„ = H{Tn+, + r„_, - 2T,,). 

The total distance apart of the extremities of the «th section of the 
wire will accordingly be 

L + \„+, - X, = L + H{T,^, + r„_i - -2T,). 

the tension of overhead vnres supported by equidistant poles. 199 

We must now make use of a well-known property of the elastic 
catenary. (See, for instance, Routh's Analytical Statics, p. 373.) 
Let X be the horizontal distance of any point of this curve 
measured from its lowest point while .Sj is the unstretched length 
of the intervening portion. Let further T^ be the horizontal com- 
ponent of the tension ; let w be the natural weight of the material 
per unit length and let E be the elastic modulus. 
We liave then 

Treating our wire as perfectly flexible we may identify I\ with the 
horizontal tension in any section and 2a; with the total distance 
apart of the extremities, while 2.§i will be the natural length of the 
portion of wire. We have accordingly 

L + H {Tn+i + ^/i-i — 22n) 
If we expand this logarithm in powers of -~, neglecting those 

-^ n 

powers beyond the third (as is permissible if the sag of the wire 
be not too great), we get 

L-\-H{ 1\^, + Tn-, -rrn) = ^' Tn + 2s,-^^, 

At a great distance from the break the tension in a section will be 
practically the same as it was before the break occurred and may 
accordingly be denoted by T^,. Our problem is thus reduced to 
solving the above equation subject to the conditions 

^0 = 0, 

say, where T is a finite quantity. 

The equation may be written briefly 

-^ n—i H" -^ n+i = a + ZOl n — 7p~^ ■ 

J- n 

Putting n = (Xi we get 

~-2{b-l)T = a. 

In order to solve the equation we shall assume that T„ may be 
expressed in the form of a series of a particular type and shall 

VOL. XV. PT. III. 14 

200 ilir Robb, Discussion of a difference equation relating to 

afterwards justify the assumption by investigating the coavergency 
of the series. Let us assume then, if possible, that 

r,. = r(i-.,|.-,,|;.-a,|;-,..). 

where a^, a«, a-^, ... G and K are quantities to be determined. 
We have then 

^ »-i — -* l^ /i'* K'^"' K'-''^ 

i„+,-lll ^^^^„ K^K-n K^K^n 

-2hT,. = -2bT{l-a,^^-a,j^^-a,j^^--), 


T„-, + Tn+,-2bTn-a + y^^ 

Thus we get 

K-^\-2{b-\-^)l = 0, 

an equation which determines K. 

The calculation of the successive coefficients (as well as the 

value of K itself) may be considerably facilitated by the help of a 

table of hyperbolic functions*. In order to do this let us write 

c s 

cosh &) = 6 + ^„ = l+ »^^jis (^'^^ + Si'iu-E) 

and ff = 

2T' esT' • 

* Good tables of these functions by C. Burrau have recently been published; 
Berlin. 1907. Georg Eeimer. 

the tension of overhead vjires .mpported by equidistant poles. 201 

Then ^ (k + -j^j = cosh co, 

and since K must be greater than unity if T^ is to be finite, 
we have 

Further H f^"" + frm) = ^'^^^ ^^<"' 

so that the value of these expressions may be at once obtained by 
the use of the tables and considerable calculation thereby avoided. 
We then have 

^ cosh 2q) — cosh ft) ^ ' 

cosh S(o — cosh ft) 

Since cosh moi — cosh co is alwa} s positive, these coefficients will 
all be positive if aj is so. The value of aj is arbitrary, but the 
presence of the constant C enables us to make it unity without 
loss of generality. We have therefore 

«i = 1, 


cosh 2ft) — cosh ft) ' 

f, 186' 

4 + 

cosh 3ft) — cosh ft) 1 cosh 2ft) — cosh &)[ ' 


iT'^ cosh 2ft) - cosh ft) K^'' 

ft I iM ^j^l 

cosh 3ft) — cosh ft) V cosh 2ft) — cosh ft)/ ^^^'^ 
Now since To = we get 

cosh 2ft) — cosh ft) 


4 + 

cosh 3ft) — cosh ft) \ cosh 2a> — cosh (o 
an equation which determines C. 

)c^-- = o, 


202 Mr Rohh, Discussion of a difference equation relating to 

This equation may be best solved by tracing the curve 

y = l-x 

cosh 2ft) — cosh ft) 

4 + 


cosh 3ft) — cosh ft) \ cosh 2ft) — cosh g) 


and noting where it cuts the axis of x. 

This series changes sigu if we substitute first x = Q and then 
x=\,BO that there must be a root between and 1 if it be con- 
vergent. Further, since the terms involving x are all of one sign, 
there cannot be more than one positive root which must be the 
quantity we require. 

Having in this way found the value of C, we may find the 

tension in the rith section by substituting -y^ for x. 

The corresponding ordinate will then bear to unity the same 
ratio that Tn bears to T. 

It may be readily shown that the curve meets the axis of y, so 
as to form an angle of 45°, and has an asymptote parallel to that 
axis and at a distance from it equal to CK. 

the tension of overhead wires supported by equidistant poles. 20S 

If T be represented by unity we shall have 

Ti represented by the ordinate at a; = j^, 

T — — - 

the general form of the curve being that shown in the figure. 
It may be proved that 

4 [ ^J<y 



7 iVl - 7 + 1 


7 = 

^T^ + s^^w^E' 

As a limiting form of the above inequality we have 

or -54134... < (7 <1. 

For the safety of the system of poles it is requisite that the 
maximum deflecting force should lie within a certain limit. This 
maximum deflecting force is clearly equal to T^. 

Section II. Investigation of Convergency. 

In order to complete our investigation we must examine into 
the question of the convergency of the series which we have 
obtained. In order to do so we write 


cosh ft) — 1 
_ s^^w'E 
~ 3T3 + s^w'^E' 

The equations connecting the successive coefficients then 

_ cosh &) — 1 7 2 
^ cosh 2a) — cosh to 2 ^ ' 

cosh ft) — 1 7 / , ., n \ 

' cosh 3ft) - cosh ft) 2 ^ ^' 

-04 Mr Bobb, Discusmm of a diference equation relating to 

Consider now the oxpiossiou 

cosh ft) — 1 

eosh DUO — cosh (o ' 

We may expand luuuerator and deuoiniuator in po\Yevs of ro 
and the series ai"e always convergent. 


cosh (0 — 1 
cosh mm — cosh to 

0)^ CO* ft)* 

- — I 1 h + . . . 

4! ^ U! 

Thns — .- " T has the limit ^ ^ for w = and for 

cosh into — cosli co //r — 1 

(0 > it has always a smaller value. 

Let 7 now be kept constant in our series and let (?/, (fa', Os\ ••• 
be the limiting values of the coethcieuts as (o approaches zeiu 

We have 

(,; = (jj = 1, 

It is thus clear that the coethcients a^, a^, a^, ... are respec- 
tively less than tu\ a/, a/ .... 

Now let 

V = \^1- 2x 

1 ., 1.3 , 1.3.5 , 

the series being convergent when 

We shall write this 

f = 1 - ?), .r - 6., a- - bs A^ - 64 a"» - . . . . 

the tension of overhead vdres supported by equidistant pjoles. 205 
Wo have further 

?/ I — 2a; 

= 1 + 2x + 2'x' + Vijr + 2^'j^ + ... , 
which iH also convergent when 


P f ^ 1- 3. 5. ..(2m -3) 
But &,, = ^j 

and HO wo may write 

1 , ^, 2.4, „ 2.4.6, , 

v'' 1 1 . o 

We have, however, on the other hand 

^ = 1 + 26i X + (36/'^ + 26,) ^;'' + (46r + 66,6, + 26,) *■'' + 
Equating coefficients we get 


while 6i = 1. 

We shall next show that if m > 2 

4 . 6 . 8 . . . 2w 


. (2m - 3) 

Wo have in the first place 


,4.6 7 


8 9 


10 11 

< fn?. 

2m 2m 4- 1 
2m — 1 2m — 1 ' 

206 Mo' Rohb, Discussion of a difference equation relating to 

Multiplying corresponding sides we get 2w + l 

< — ^ — ...{2m -I) 
if m > 2. Or 

4.G.8...27?i „ 1 

<-' 'in- 

1.3. 5. ..(2m -3) 4 

Thus finally 

4.6.8... 2m 

< m-. 

For m = 2 this inequality becomes an equality. 

It follows that 6.J, bs, h^, h, ... 

are respectively greater than 

Oo, a/, a/, a^, ... 

where «/= 1, 



a; = 

^' = 2(F:ri)T^(^«^" + 6">^')' 

and 7 is less than unity. 

A fortiori 

h, h, h^, ... 

are respectively greater than 

0-2, a-i, «4, ••• 

and therefore for values of 

the series 

y = 1 — a- — — asOf — a^a;-* — . . . 

converges more rapidly than the series 

1 , 1.3 . 1.3.5 , 

v = l-a:-^^^v--^ar--j^cc^-.... 

If we include terms up to that involving a--'" the remainder for 
this latter series is known to be numerically less than 

1.3.5 ...{2m-l) x'^+' 
m + l\ 1 -2a;' 

the tension of overhead wires supported by equidistant poles. 207 

which is accordingly a superior limit to the error involved if we 
neglect the powers of x above the mth in the expansion of y, 

We have in fact for such values of x 

T [1 — -rp — ai^f^„ — as 

\/l — 2x <y <{l — x). 

If now we take a value of x less than ^ and form the series 

T (1 — X — a^x^ — a^x^ — • • •) 

it will represent some value of the function T^ where, however, 
n is unknown and is not necessarily an integer. 

We can similarly form the series 

\Aj %Aj *Aj 

which will also converge and will represent T,i+i. 

Now Tn is positive and the series which represents it is 
absolutely convergent and therefore its square forms a convergent 
series with the same radius of convergency. Now it is known (see 
Bromwich's Theory of Infinite Series, p. 216) that the circle of con- 
vergence of the reciprocal of a power-series is either the same as 
that of the original series, or else reaches up to the zero of the 

given series which is nearest to the origin. Thus jfj-^ forms a 

convergent series, since the absolute value of x does not extend as 
far as a zero of the function T^. 

We thus see that 

a + 2.0 In — jf-^ — In+i 

forms a convergent series in x. 

But this will represent Tn-i which is accordingly given by our 
series and must be absolutely convergent so far at least. 

If now it should so happen that Tn-i is positive, we may repeat 

this process and ™ — - will give a convergent series in x and 

-^ n—i 

therefore T„_2 is given by a convergent series. 

If, however, Tn-i is negative we have passed over a root of the 


and consequently ™ — - will no longer converge and the series 

will not give Tn-^. 

208 Mr Rohh, Discussion of a difference equation relating to 

Now the series is continuous within the limits of convergency 
and therefore there will be a definite value of w which satisfies this 
equation and is the quantity denoted by C. 

Thus KG is the radius of the circle of convergence. 

Since Vl — 2a; < y < (1 — a-) for values of «; less than ^ it follows 
that ^<C<1. 

We have, however, mentioned that 

7ivl-7 + lj 
This result is obtained by considering the series 
w=l — cc — ttoX'^ — a/a? — ... 
which is the limit of the series 

y = 1 — a? — rto oc:- — «3 .^■^ — . . . . 

The series for 7U can readily be shown to satisfy the differential 

A solution of this equation may be obtained in finite form for 
the case where 

w — 1 

and -^ = — 1, when x = 0. 


This solution takes the form 

"2 2 

W\ — 7 wi + V(l - 7) w + 7]N/r^ (1 - w) _ iVl — 7 + 11^1^7 
{w4 + V( 1 - 7) w + 7} ■ 4 

which oives w = 

when x = ^\ ^^ IVT^ 

and it is clear that 

w < y < 1 

for values of x less than the above*. 
It follows that 

4 f ■ Vt 


7 (Vl -7+1 

■Vi-7< C <1. 

* The expansion of ic in powers of x must converge up to this point, since there 
is no singularity of the function w anywhere nearer to the origin. 

the tension of overhead wires supported by equidistant j)oles. 209 

The complicated form of the solution of the differential 
equation renders it less convenient than the simple function 

V = ^\ — 2x 

for estimating the degree of convergence, although the former 
is valid over a greater range and gives a closer approximation. 

Concluding Remarks. 

In the foregoing investigation we have treated the problem as 
a statical one in which an equilibrium condition has been attained. 

The extent to which this supposition is permissible will depend 
upon the circumstances of the break, and the rate at which energy- 
is dissipated in the system. If the wire is suddenly cut the nearest 
pole will initially be subject to a force equal to T, but this force 
will quickly diminish before it has produced much effect in bending 
the pole. 

In any case the dynamical problem appears too complicated to 
lead to trustworthy results even if the purely mathematical diffi- 
culties should be overcome. 

Another important point is the actual number of poles which 
must be passed over, counting from the break, before the statical 
tension T^ may be practically regarded as equal to T,^ or T. 

It is clear that this depends almost entirely on the value of K, 
and n will be very large if K is nearly equal to unity. 


We may estimate the size of n by considering that -^ must be 

negligible in comparison with unity. If quantities less than e be 
regarded as negligible then we must have 

That is n> 

It may perhaps be 
value of Ti is given by 

log C — log e 


\og K 
It may perhaps be worthy of note that a superior limit to the 

X f xY / xy 




4f V7 l^rr^ 

x = - J Wi-v 

7(\/l-7 + l| 

210 Mr Dixon, On a property of summahle functions. 

On a property of summahle functioiis. By A. C. Dixon, Sc.D., 

Trinity College. 

[Received 22 March 1909.] 

[Read 3 May 1909.] 

1. It is a known theorem*, due to de la Vallee-Poussin, that 
if f{x) is a limited integrable real function of x in the interval 
(— TT, tt) and if 

IT'" 1 /''" 

ao=~l f{t)dt, an = -\ f(t) cos ntdt, 

1 f'^ 

hn = - \ f(t) sin 7itdt, 

IT J -^ 

then ^tto^ + 2 (a,j^ + b^^) is a convergent series, whose sum is 

It is also known that if a^, a/, ...,hi ... are the Fourier con- 
stants of a second such function (f) {x), formed from it in the same 
manner as a^, «!, ..., bi, ... from f(x), then 

^ tto fio' + 2 (a„ an + bn bn) 
is a convergent series, whose sum is 

ir f{t)4>{t) 


If we suppose /(^) to be periodic, with period 27r, and take 
^ (^) —f^^ + 2/)' '^® have 

1 f" 

/(i + 2/) cos ?iic?^ 


/(^)cos 71 (^ — y^dt 

= a^ cos ny + &« sin ny, 
and 6„' = 6„ cos ny — an sin ny similarly ; 

also ao = ao. 

Thus an an + bn bn = (a,i^ + &,i^) cos ny, 

1 /"IT OO 

and - f(t)f{t +y)dt = \ao^ + X (an' + bn') cos ny. 

"^ J -TT 1 

* For proof and references see Hobson, Functions of a Real Variable, pp. 715-7, 
723-5 ; B6eher, Annals of Mathematics, ser. 2, vol. vii. p. 107. 

Mr Dixon, On a property of summahle functions. 211 

This series is uniformly convergent for all real values of y, 
and hence its sum is a continuous function of y ; putting x for y 
we have that 

f(t)f{t + x)dt 

is a continuous function of x, if f(x) is any limited integrable 
function, with the period 27r. 

The first object of the present note is to give a proof of this 
theorem, independent of the Fourier theory. 

A special case is that 

f(t)f(t-^x)dt=r {f{t)Ydt 

J —IT 

{fit + x)Y dt, 

from which it follows that 

Lt r {f{t + x)-f{t)Ydt = 0. 

X^O J -IT 

This special case will be proved first, and the more general 
theorem then derived from it. The method of proof is applied 
to unlimited, as well as to limited, functions, and thus it is possible 
to prove de la Vallee-Poussin's theorem for all cases in which it 
has a meaning. 

2. Let f{x) be a limited summable function in an interval 
{a', h') which includes a, h as internal points, and let U, L be its 
upper and lower boundaries in {a, h). Divide the interval {L, U) 
into n—\ equal parts, at a^, as ... «.«-!> and let a^= L, an = U. 

Let the set of values of x in (a, b) for which ar-i<f{oc) ^ a^ be 
called er{r = l, 2 . . . %). 

Enclose e^ in a set of intervals A,., not overlapping, and the 
complementary set 6^(e,.) in intervals F^, not overlapping, so that 
Ay, F^ have a common part < a. This can be done, for f{x) is 

Let the intervals of A,., in descending order of length, be 
Ki, ^n--- S'lid take an integer p, such that 

I S,,^>A,-e (r = l, 2...n). 

m = l 

Let er^m denote the part of hr,m which is also in F^. 

The similarly formed system of sets and intervals in 
{a-\-6, h + 6), shifted back a distance 6, will serve for the function 
f(x+ 6) ; let them be distinguished in this new position by dashes, 
so that SV,m is S^.m ill the new position. Of course 6 <h' —h. 

212 Mr Dixon, On a property of summable functions. 

Then for any x which is common to §,.„,, and h',.^m and which is 
not in r,. or TV, 

\f{x + e)-f{x)\<{U-L)l{n-l). 

Now the part common to Sy^,„ and h'r,m is K,m— 0, and of this 
at most 2€r,m lies in F,. or TV- 

Hence \f(x + 6) -f(x) \<(U- L)l{n - 1) 

over intervals, E, which are together 

. n p 

7'=] m = l 

Also S X Br,m>'X^r — ne>{b — a)-n€, 

r m=\ 

P P 

The sum of the intervals E is therefore within 
n (e + 2a) + np6 
of the length of the whole interval (a, b). 

Again, \f(x + 0)—f(x)\ can nowhere exceed U—L. 

Hence I {/(^ + ^)—/(a;)}^(ia; does not exceed ^ 

J a 

{^;^)\h-a) + (U-Ly{n{e + 2oc) + np0], 

the first term arising from E, and the second from the rest* of 
(a, b). 

Here we may give n any fixed value, and put a=6= — , so 

fixing p ; then if ^ < — - , the whole will be < - of a quantitv 
n-p n n J 

independent of n, and will tend to zero as n is increased. 

Hence Lt I {/(a; + ^)— /(ic)}2(^ic = 0, when/(a;) is any limited 
e-9-o -' a 
summable function. 

The same method shews that 

I \f(x+d)-f(x)\9dx 

* Here, as in § 4 below, such end-points of the intervals constituting e,., „ as 
lie -within 5,.^ ^ form an enumerable set, whose measure is zero, so that it does 
not matter whether they are included, excluded, or counted twice over. 

Mr Dixon, On a pi^operty of siimmahle functions. 213 

tends to zero with 6, if g is any positive number, and that the 
same is true of 


J a 

where Fx is any function that is finite when x is finite and 
tends to zero with x. 

3. To prove that 


f{t)f(t + x)dt, 

say (f) (x), is continuous, if (a, h), {a + x, h + x) are both included 
in (a', h'), we have , , . 

(^ (^) - (^ {y) = f /(O [fit + ^) -fii + y)] dt, 

J a 

and therefore 

{<!> (x) - cf> {y)Y < f {f{t)Y dt r [fit + x) -fit + y)Y dt, 

J a J a 

in which the first factor is finite, and the second tends to zero with 
X — y hj what has been proved. 

Hence (f)(x) — ^ (y) tends to zero with x — y, and (f) (x) is a 
continuous function of x. 

If we now put a =—77, b = 7r and suppose /(^) to have the 
period 27r, it is easy to find the Fourier expansion of (j) (x). 

First, (f) (x) is an even function of x. 


fir rir r-ir 

I <^ {x) cos nxdx = 1 I f(t)f{t + x) cos nxdtdx 

J —TT J —irJ —n 

f(i)f (y) COS n(y-t)dy dt 

J —TT J —IT 

— I /(O co^ '^^^dt X I f(y) cos nydy 

J —TT J —TT 

+ I f(t) sin ntdt x I fiy) sin nydy. 

J —TT J —IT 

Hence the Fourier constants of <f) (x) are 

7^ao^ TT (fti^ + 61^), TT {a.^ + b^^), . . . 
0, 0, ... 

* In calculating I I ^/(« + .T)/(t) cos n.rdirf.T, we first change the order of 

integration, and this is jiastified for/(.x-) and f{x+y) are both summable in any 
rectangle in the xy plane : the set for which k>f{x)>l consists of lines parallel to 
the y axis and the set for which k>f(x + y)>-l of lines which make equal intercepts 
on tlie axes. 

214 Mr Dixon, On a property of summahle functions. 
if those oi f{x) are 

tty, Cll, di^y ..., 

61, h, .... 

n If'" 

Since ifto' + t {an"" + K^) < - {/(^)}' ^^ 

1 TT J -n 

for all values of w, the Fourier series is absolutely and uniformly 
convergent, and since (}){x) is continuous, the sum of the series is 
equal to (f) (x), that is, 

(f){x)= I irao^ + TT 2 (ttn^ + bn^) cos nx. 

(Hobson, F. R. V., p. 713.) 

4. Suppose now that f(x) is not a limited function, but is 
still summable in an interval (a', h'), which includes a, h as 
internal points. It will be proved that 

\\f{x + e)-f{x)Ydx 

J a 

tends to zero with 6, if I \f{x)Y dx exists. 

J a 

Take a finite quantity h, which will afterwards be made to 
diminish without limit. Let er{r = 0, ± 1, ± 2 ...) denote the set 
of points in (a, h) where {r—l)h <f(x)^rh. 

Take a whole number n, so that I {/ (^)j^ dx, taken over the 

set complementary to ei^n + ••■ +&0 + S1+ ... +en, is < 7. 

Enclose e^ in a set of intervals A,., not overlapping, and C(e,.) 
in intervals F^, not overlapping, so that A^, F^ have a common 
part not exceeding a/(2?^+l)^. The sum of these common parts 
for all values of r is then < 3a. Then we shall have 

Ao+Ai + ...+A„ 
+ A_i + . . . + A_„ > (6 - a) - /3, where /3 = y/n^'h^ 

Let the intervals of A^, in descending order of length, be 
Sn, 8r2". and take a whole number p, such that 

Z 8r,m>^r-e (r = 0, ±1, ...±n). 

Let er^m be the part of h^^m which is also in F,., and let the 
dash again indicate a displacement Q to the left. 

Then for any x which is common to hr^m and SV,m and is not 
in F,. (jr F',., 


Mr Dixon, On a property of summable functions. 215 

and as before \f(x + 0)—f(a;)\<h over intervals E which are 

r= —n m—\ 

In this expression SlSS^,^ > ^l^r — (2w + 1) e 

>(6-a)-/3-(2w + l)e, 
22er,m< 3a, 
and the intervals E fall short by less than 

/8 + (2^ + 1) e + 6a + ^ (2/1 + 1) ^ 
of the whole interval (a, 6). 
The value of 

\ [f{x^-6)-f{x)Ydx<{h-a)h\ 

J E 

For the rest of (a, h) we have 

/{/(^ + 0) -f{x)Y dx^2 j{f(x)Y dx + 2J{f(x + 0)Y dx. 

To the first term of this, the set where \f{x)\ >nh contributes 
a quantity < 27, and the rest a quantity 

< 2n-'h''{l3 + i2n + l)e + 6a+p{2n+l)0}; 
treating the other term similarly, and putting 7 for w^A^/3, we have 

[ {f(x + d) -f{x)Y dx <(b-a)h' + 87 

+ ^n%'' [{2n + 1) e + 6a + ^ {2n + 1) 6]. 


Since now I {f{x)Ydx 

J a 

exists we may take 7 = /^^ thus fixing n. 

1 1 

We can also take a = — , e = 

n" w 

the latter condition fixing p. Then if ^ < -^ , the whole is less 

than a certain constant multiple of h^, and can be made as small 
as we please by diminishing h. 


Lt I {f{x + e)-f{x)Ydx = o, if f {f{x)Ydx 

exists, f{x) being a function which is summable in an interval 
(a, b') which includes (a, b). 

VOL. XV. PT. III. 15 

21(5 Mr Di^on, On a propei'ty of summable functions. 
The same method enables us to prove that 

Lt f\f{a' + e)-f{xyilv = if f \f{x)\da; 

e-*.0 J a J a 

exists, by means of the inequality 

|/(.r + 0) -fiw) I < \f{w) I + \;\x + e)\. 

5. The deduction of the continuity of 

1 f{t + x)f{t)dt, 

J a 

and that of the Fourier expansion for it, still hold good, and in 
particular it follows that the series ^a^ + S (rt,f + t,f) converges 
to the sum 

even when f{d') is unlimited, if this last integral exists and is 

6. It follows from the results of § 2 that a necessary condition 
for a limited function /\it') to be summable is that the superior* 
integral of \f{'i'+(^)—f{ii^ tend to zero with 0. The question 
is at ouce suggested whether this condition is suthcieut, and if not 
whether a satisfactory detinition can be given for the integral of a 
function which satisfies this condition, but is not assumed to be 

* In Lebesigne's sense, see Hobson, F. E. V. p. 577. 

Mr Orange, On certain 'phenomena, of the kathode region. 217 

On certain phenomena of the kathode region. By J. A. Okange, 
B.A., Major .Scholar of Trinity College. [Communicated by 
Professor Sir J. J. Thomson.] 

[Bead 17 May 1909.] 

(Plates IV— IX.) 

In the discharge through rarefied gases, the appearances 
surrounding the kathode seem to be quite independent of the 
form and situation of the anode, and also of the shape of the 
containing vessel, provided that the latter does not approach too 
near to the kathode. For instance, if one arranges any kind of 
kathode, of linear dimensions up to about 4 cms., in the middle 
of a glass bulb of about 10 cms. diameter, the various luminous 
effects associated with the kathode and known as glows and rays 
(together with the secondary effect of phosphorescence on the 
walls of the vessel) appear to have no relation to the position of 
the side tube which contains the anode, but are determined solely 
by the characteristics of the kathode, the intensity of the discharge, 
and the pressure of the gas through which it passes. 

Throughout the whole range of what are termed low pressures 
(pressures less than 1 mm. of mercury, say) the surface of demar- 
cation between the Crookes' dark space and the negative glow is 
one of the most conspicuous features of the region and, moreover, 
its form is of considerable theoretical interest. The rajs which 
have been observed in the neighbourhood of the kathode fall into 
two classes, the first, which is now fairly well defined, consisting of 
the kathode rays, rays that are twisted readily by the application 
of a weak magnetic field, while the second consists of a number 
of rather indefinite radiations to which Goldstein* has applied the 
name of ' The Canal Ray Group.' 

Both classes of rays are in a sense more difficult of treatment 
than the glows and dark spaces, for there is no one characteristic 
by which a radiation may be apprehended, throughout the whole 
range of pressures at which it undoubtedly exists. For example, 
kathode rays have a maximum of luminosity at a certain pressure. 
If the exhaustion is carried further the rays gradually become less 
luminous, but at the same time another property is coming into 
evidence, namely, the power of producing phosphorescence on the 
glass, until finally we have quite invisible rays manifested solely 
by the vivid phosphorescence at their termination. The canal 
ray group shows luminosity within a still more restricted range of 
pressure and gives rise to much inferior phosphorescent effects. 
By piecing together the rather fragmentary evidences of the 

* E. Goldstein, Verhandl. d. D. Physik. Gesellsch. (iv), p. 228, 1902; Phil. Blag. 
March 1908, p. 372. 


218 Mr Orange, On certain phenomena of the kathode region. 

various rays it is possible, nevertheless, to map out their courses 
with considerable precision. 

Much of the work on the distribution of the kathode rays has 
been performed by Goldstein. His paper, "Ueber den Einfluss 
der Kathodenform auf die Vertheilung des Phosphorescenzlichtes 
Geissler-'scher Eohren"* deals very thoroughly with the phos- 
phorescent patterns produced on the glass walls of discharge- 
tubes by kathode rays arising from concave kathodes of various 
geometrical outlines. 

Somewhat related to the same subject was the work of 
Campbell Swinton-f* on the kathode rays from concave carbon 

A much more recent paper by Goldstein J deals with the 
phenomena of the double or sandwich kathode, while supple- 
mentary observations have been made by Kunz§. 

The subject has also been treated in a rather different way by 
Prof. J. J. Thomson II. 

The general method in most of this previous work seems to 
have been to obtain phosphorescent effects and to establish the 
paths of the rays from these. The experiments described below 
were intended to demonstrate the paths as far as possible directly 
by virtue of the luminosity of the rays themselves. 

The primary object of these experiments was to test the view 
put forward by Prof. J. J. Thomson of the beams of rays obtained 
with a double kathode composed of equilateral triangles. He 
observed that well-marked pencils of kathode rays arose from the 
middle points of the sides of the triangles, while minor ones 
proceeded from the corners. His explanation IF was that the rays 
will occur principally in the regions where the lines of force are 
straight or nearly straight, since in such circumstances any positive 
ions produced by the kathode rays will strike the kathode very 
near the source of those rays, which would not be the case in 
regions of strongly curved lines of force. 

In my first experiment I employed a double triangular kathode 
of extremely unsymmetrical outline, the lengths of the sides of 
the triangles being 36, 24 and 16 mm., i.e. a :h = b : c = d : 2. 
It was thought that with this arrangement the straight lines of 
force would occur, not at the middle points of the sides, but at 
other points which could be determined roughly. Since, however, 
the field is due not only to the charged kathode but also to a 
large extent to the distribution of charge throughout the region, 

* E, Goldstein, Wied. Ann. xv. 1882, p. 254. 

t A. A. Campbell Swinton, Proc. Roij. Soc. Vol. lxi. (1897), No. 370, p. 79. 

+ E. Goldstein, Phil. Mag. March 1908, p. 372. 

§ J. Kunz, Phil. Mag. July 1908, p. 161. 

II J. J. Thomson, Phil. Mag. Oct. 1908, p. 657. 

H Ibid. p. 666. 

Mr Orange, On certain phenomena of the kathode region. 219 

the question is more complicated than at first sight appears. For 
other reasons the experiment failed with regard to the primary 
object, as will appear in the following account. 

Fig. 1. 
Experiment I. 

The discharge vessel employed was of the form shown in Fig. 1. 
It was in continuous connection with a Toepler pump to which the 
usual phosphorus pentoxide bulb was attached. The gas used 
was generally air* but for a special purpose hydrogen was introduced 

* At times apparatus was used in which many joints, made air-tight by the use 
of sealing wax and varnish, occurred, and in consequence the gas was largely 
carbon monoxide. 

220 Mr Orange, On certain phenomena of the kathode region. 

at a later stage ; this was attained by having a small bulb con- 
taining dry sodium formate in connection with the apparatus and 
heating to 250° C. when the hydrogen was required. 

The kathode is shown separately in Fig. 2 ; it was made of 
aluminium and carried on a lead of the same material protected 
by a glass tube. 

An induction-coil with the common interrupter maintained the 
discharge and in the usual way a condenser was connected to the 
interrupter, but it was found necessary (with the higher gas 
pressures at least) to insert a ' point and plane ' spark gap in the 
secondary circuit, to secure freedom from reversals. 






Fig. 2. 

At first it was thought that sufficiently accurate records of the 
appearance of the discharge could be obtained by sketching, but 
owing to the glare this was painful to the eyes and did not give 
very satisfactory results. Recourse was then had to photography 
and as a rule little difficulty was encountered. The camera 
employed could be extended considerably and consequently could 
be set up very near to the discharge-tube, so that photographs 
were obtained of nearly natural size. Using Imperial Ortho 
plates, exposures of from 2 to 5 minutes were given, the aperture 

being -. 

Fig. 1, PI. IV*, shows the peculiar appearance of the kathode 
region when the Crookes' dark space envelopes only the corners of 
the triangle. [Cp. Kunz, loc. cit. Fig. 16.] 

* It should be noted that certain features of these photographs are quite acci- 
dental, being reflections from the glass discharge vessel, e.g. the eye-shaped patch 
of light opposite the shortest side of the triangle, and two rectilinear markings 
opposite the side of intermediate length. 

Further, the positive column, which extends a variable distance down into the 
bulb, should be clearly distinguished. 

Mr Orange, On certain phenomena of the kathode region. 221 

This would indicate that at this pressure the discharge is 
taking place almost entirely from the corners of the kathode, the 
probable explanation being that the electrostatic field at this 
stage is somewhat similar to the simple field due to a charged 
triangular conductor. If this is so, those portions of the sides of 
the kathode which are free from dark space will correspond very 
well with the regions of weakest electric intensity. But these 
regions of low intensity are the places where the lines of force are 
straightest. Hence, when the mean free path in the gas is suffi- 
ciently great for the untrammelled formation of kathode rays, the 
discharge will tend to occur to a greater extent than previously 
from those parts (according to Prof. Thomson's view given above), 
and the Crookes' dark space will surround the whole triangle, 
although it will be somewhat narrower opposite these places. 
[e.g. ctr. Figs. 1 and 2, PL IV.] 

In the next photograph, Fig. 2, PI. IV, the pressure is a little 
lower and the kathode rays have become visible. They appear to 
come off from practically the whole lengths of the sides of the 
triangle, and show maxima of luminosity at certain places. It 
seems only too probable, however, that the three connecting pins, 
the ends of which appear in the photograph, play a large part in 
determining the positions of these maxima. Notice in this and 
the following photograph, Fig. 1, PI. V, the dimpled boundary of the 
Crookes' dark space opposite each of the three sides of the triangle, 
as referred to above. 

The next photograph. Fig. 2, PI. V, has a very vague appearance 
because at this stage the kathode rays, although now past their 
maximum of brightness, are still fairly active photographically, 
by virtue of their bluish colour, whereas the canal rays, in spite 
of their prominence visually, are inadequately recorded by the 
camera owing to their reddish colour. We thus have a medley of 
two kinds of rays which it would be difficult and unprofitable to 
unravel at this stage. The beginning of the green phosphorescence 
due to kathode rays is visible in this photograph in three patches 
corresponding to the three sides of the triangle, but the next view. 
Fig. 1, PI. VI, associated with an increased exhaustion, shows the 
phosphorescence very well. The blaze of light which masks the 
kathode in this case, represents the phosphorescence on the glass 
wall nearest to the camera. The actual space within the vessel is 
almost free from luminosity, but it is still possible to make out 
the boundary of the Crookes' dark space and a few traces of the 

The last photograph of this set. Fig. 2, PI. VI, is certainly the 
most interesting owing to the distinct appearance of the ' canal 
rays ' [so-called by Goldstein*]. It corresponds very nearly to 

* E. Goldstein, Phil. Mag. March 1908, p. 378. 

222 Mr Orange, On certain 'phenomena of the kathode region. 

Fig. 2, PI. V, but hydrogen was used instead of air in order to 
obtain canal rays of a more reddish colour than those in air; 
further, a yellow glass screen, which cut out the blue end of the 
spectrum, was used in conjunction with orthochromatic plates. 
It should be remembered that the kathode rays are still just 
visible at this stage, as shown in Fig. 2, PI. V, but are suppressed 
in the present example owing to the photographic method used. 
[An exposure of 40 minutes was necessary and this gave rise to 

Fig. 3. 

difficulties at first owing to the strong tendency of the vacuum to 
'harden' with continued running of the discharge. By judiciously 
fixing the initial pressure of the gas, however, it is possible to 
obtain steady conditions if the discharge is given a preliminary 

The configuration of the canal rays can be made clearer by 
means of a diagram. Fig. 3*. As the pressure is reduced still 

* It may be stated here that subsequent experiments have shown that the three 
connecting pins do not affect the boundaries of these beams. 

Mr Orange, On certain phenomena of the kathode region. 223 

further, the rays extend through a smaller distance from the 
kathode ; the boundaries of the beams also change gradually, so 
that at some distance from the kathode the beams become more 

In previous work, kathodes of symmetrical or nearly sym- 
metrical outline have been used, and consequently w^hat one might 
call the roots of the beams of canal rays have been hidden by the 
kathode. The shape of these has however been inferred from 
markings which are found on the inner surfaces of the kathode, 
after the discharge has been running for some time *. [ Vide Fig. 4, 
taken from Goldstein's paper.] The case described above indicates 
that the boundaries of the beams are similar in character whether 
they fall within the outline of the kathode or not. 

Fig. 4. 

But, arguing from the cases of more regular kathodes, Gold- 
stein, loG. cit., and Kunz-j- have advanced an explanation of the 
curved boundaries which only holds when the curvature occurs 
within the kathodic interspace. 

Goldstein says, " From the concave boundary of the traces and 
of the pencils themselves, it may be inferred that the rays pro- 
ceeding from any side are subject to an attraction due to the 
neighbouring sides. We may, for example, imagine that in the 
case of the square the rays are originally convergent along straight 
lines, somewhat after the fashion indicated by the dotted lines in 
Fig. 7 [Fig. 4 of the present paper], and that it is in consequence 
of the attraction exerted on them by the adjacent sides that they 
assume the actually observed form (shown by the full lines)." 

* E. Goldstein, loc. cit. p. 377. 

+ J. Kunz, Phil. Mag. July 1908, p. 180. 

224 Mr Orange, On certain phenomena of the kathode region. 

It would seem now that no such simple explanation based on 
the geometry of the kathode will suffice. Each beam is sym- 
metrical about the central normal to the corresponding side of the 
triangle, although the two corners which bound that side differ 
considerably. Thus we cannot invoke the aid of the electrostatic 
field ; this is shown also by the way in which the two narrower 
beams cross each other, at a of Fig. 3, as if operated quite inde- 
pendently. The latter fact is also opposed to the supposition that 

Fig. 5. 

the constituent particles of the beams are strongly mutually 
repulsive, a supposition that might have been advanced to account 
for the curved boundaries. 

The author puts forward the suggestion that the latter are 
similar to caustic curves, that is, are the envelopes of straight rays, 
as shown diagrammatically in Fig. 5. 

We thus avoid the necessity for supposing the beams to be 
acted on by peculiar systems of forces, systems which would seem 

Mr Orange, On certain pheoiomena of the kathode region. 225 

almost impossible. If, then, we consider the beams to be con- 
stituted of straight rays instead of curved ones, the problems 
which face us are two much simpler ones. 

(i) To account for the directions of the constituent straight 
rays, and 

(ii) To account for the occurrence of the luminosity of the 
rays after, and only after, they have passed through the kathodic 

With regard to the first question, let us consider the canal 
beam which arises from the longest side of the triangle and 
runs towards the left of the picture (Fig. 2, PI. VI). 

Adopting Prof. Thomson's explanation of the mutual inter- 
dependence of kathode and canal rays, we suppose this beam to 
have its origin in the region to the right of the kathode. It would 
be interesting then to know where the kathode rays which, starting 
from the longest side of the triangle, run to the right, accomplish 
the ionization which gives rise to the canal rays. 

Reference to Fig. 1, PI. VI, tells us roughly where the kathode 
rays in question excite phosphorescence on the glass vessel. This 
has been indicated by the dotted line fg in the diagram, Fig. 3. 
There is thus at least a rough correspondence between the region 
where ions are produced by the kathode rays and the backward 
prolongation of the visible canal rays. The same argument 
seems to apply to the other two canal ray beams. (It is evident 
however, that one limit of the phosphorescence, at e, Fig. 3, is 
rendered uncertain by the occurrence of the anode side tube at 
that part of the bulb.) 

The second question, that of the luminosity of the canal rays 
after passing the kathode, remains to be considered. If the canal 
rays be regarded as positive ions which move up to the kathode 
with continually increasing velocity and, after passing the kathode, 
lose their velocity by the reverse process, it is indeed difficult to 
account for their luminosity occurring only after passing the 
kathode. It can be shown quite readily, however, that the posi- 
tive ions are much more likely to be neutralized when moving 
away from the kathode than when approaching it. For in the 
former case they encounter negative ions moving in nearly the 
same direction, while in the latter they encounter them travelling 
in nearly the opposite one. Thus if recombination is associated 
with luminosity, as is probable, we can see why the canal rays are 
visible only after passing the kathode. We may consider the 
recombination to occur entirely within a short distance of the 
kathode, in which case the visible length of the rays can be 
explained by supposing the ions to vibrate for about 5 x 10~^ sec, 
or we may consider that recombination occurs throughout the 
whole visible length of the beam. 

226 Mr Orange, On certain phenomena of the katliode region. 

The former view seems better as yet, because 

(1) the luminous beams do not seem to be under the influence 
of the electrostatic field, and 

(2) Kunz* states that "Prof J. J. Thomson, who applied a 
very strong (magnetic) field to these rays, could find so far no 
deflexion at all." (The rays referred to were obtained with an 
equilateral triangular double kathode.) 

It was next proposed to devise apparatus in which the two 
kathode plates were not connected by pins, but carried on separate 
leads, and since we did not know definitely by what amount the 
plates should be separated, to secure the best results, it was 
decided that this should be susceptible of adjustment while the 
discharge was running. 

Experiment II. 

The apparatus is represented in Fig. 6. One anode A and one 
kathode B are supported from above while the other kathode G 
and the anode D, which are mechanically connected by ebonite, E, 
can be moved up and down by means of a barometer column with 
moveable reservoir. (The float H, which is used in this process, 
makes contact between the kathode lead and the mercury of the 
column. The anode lead is attached to the fine spiral of wire G, 
so that it is readily moveable.) 

The kathode plates were similar to those used in the first ex- 
periment but were bevelled as shown in the figure, with the object 
of simplifying the section of the kathodes and hence of the elec- 
trostatic field. The two plates, or rather their connections, were 
joined externally by a wire. The two anodes were used in de- 
termining whether the kathode region were quite independent of 
the situation of the anode. On observing that this was so, the 
lower anode was disconnected and the upper one alone was em- 
ployed throughout. 

Although it was possible to obtain views of the kathode region 
similar to those of the first experiment, photography in this 
direction, i.e. vertically downwards, was out of the question owing 
to the inconvenience of the arrangements. It could be seen, how- 
ever, that the canal rays formed beams very similar to those 
obtained with the original double kathode. 

The canal rays are most conspicuous when the separation of 
the plates is about 3 mm., but they are observed quite easily with 
separations of from 1 to 15 mm. With the larger degrees of 
separation the beams are more convergent than those described in 
Expt. I. 

* J. Kunz, loc. cit. p. 177. 

Mr Orange, On certain phenomena of the kathode region. 227 

Fig. 6. 
The apparatus is shown in two parts, the upper one lying to the left. 

228 Mr Orange, On certain phenomena of the kathode i^egion. 

The inconvenience of the apparatus in the respect mentioned 
above was amply compensated for by the ease with which the 
region could be viewed in other directions (that is to say, in hori- 
zontal directions). Of the appearance in one of these directions, 
viz. that showing the kathodes lengthwise, there is little to say. 
Fig. 6, Plate IX, shows the one stage of any interest ; the form of 
the Crookes' dark spaces in the kathodic interspace is peculiar, 
but it seems to be quite in accordance with the views previously 

Examination of the region in the remaining principal direction 
revealed much more interesting features (Pis. VII and VIII), and 
what follows refers entirely to appearances viewed in this way. (i.e. 
by looking horizontally so that the line of sight is parallel to the 
longest sides of the kathodes, these longest sides lying to the left, 
while the obtuse angles of course fall on the right.) 

The photographs cited are selected from a large number of 
records taken. In Figs. 2 and 7, PL VIII, the positive column in- 
trudes but does not seriously mar the view; it would appear to have 
no direct connection with the phenomena discussed in this paper. 
The Crookes' dark spaces are in all cases clearly defined, and it is 
noticeable that while they are still unfused, as in Figs. 1, 2 and 6, 
PI. VII, the thickness of the dark space is greater opposite the 
remote faces of the kathodes than it is over the interfaces. 

The striking feature, however, in most of this series, is the 
distribution of kathode rays in the form of a very sharply-defined 
cross of St Andrew's. The pencils are especially well defined on 
the left side, that is in connection with the longest sides of the 
triangles. On the right some slight confusion occurs owing to the 
way in which this part of the triangle is viewed. The system of 
rays really forms two sheets, somewhat like slightly truncated 
pyramids, the base of the lower one being visible at the lowest 
pressures as a phosphorescent trace which encircles the bulb like 
a line of latitude (Figs. 2 and 7, PI. VIII). The pencils are 
remarkably restricted transversely at the lower pressures, e.g. 
Fig. 7, and, moreover, they pursue a slightly curved path. In 
all cases where the two Crookes' dark spaces either adjoin each 
other or are fused together, kathode rays are also emitted abun- 
dantly along the median plane of the interkathodic space, e.g. 
Fig. 1, PL VIII. 

I think we may correlate the oblique rays with a phenomenon 
described by Kunz*. Kunz used as kathode a hollow cylinder and 
observed on the containing vessel phosphorescent rings opposite 
the mouths of the cylinder. If the rays described above correspond 
to those producing Kunz's rings, then the latter's explanation 
of the phenomenon must be wrong, as a reference to his diagram f 
will show. 

* J. Kunz, loc. cit. pp. 164 et seq. t Ibid. p. 170. 

Mr Orange, On certain -phenomena of the kathode region. 229 

The way in which the pencils change with the gas pressure and 
the separation of the plates is easily summarized qualitatively : 
The inclination of the rays to the plane of either kathode 

(1) increases with the distance separating the plates, and 

(2) increases with the pressure. 

There is a transition at a certain stage of exhaustion ; at the 
higher pressures the rays being sharply bounded on one side only, 
while at lower pressures they form true sheets which are well- 
defined on both sides. 

[Figs. 1 and 6, PI. VII, Fig. 3, PI. VIII are typical o{ higher pressures, 
„ 2 and 7, „ „ „ „ rather lower „ 

„ 3 „ is „ „ transitional „ 

4 „ „ „ „ still lower „ 

5 „ Fig. 6, PI. VIII are „ „ low „ ] 
Figs. 4 and 5, PI. VIII are prints from a single negative. The first 

shows details of the rays near the kathodes very well while the 
second shows up the general appearance. At this stage the two 
" oblique " beams on the left as well as the median beam are 
practically horizontal. 

In seeking an explanation of the pencils, let us first disregard 
the origin of the rays and consider only their directions and 
curvature. If we except the comparatively high pressures — at 
which the rays are ill-defined — it may be observed that the 
asymptotes of the rays always pass approximately through the 
central point of the kathode interspace. This would imply that 
the electrostatic field is determined largely by the existence of 
free charge in the region containing the kathodes, as distinct 
from the charge on the kathodes themselves, and, in fact, that 
in the cases considered there is a region of negative charge 
corresponding roughly with the brightly luminous part of the 

It has been shown by various workers that the electric intensity 
in the ordinary Crookes' dark space is considerable at all points 
but increases rapidly as the kathode is approached ; Schuster's* 
experiments indicate that there is a distribution of free positive elec- 
tricity in the dark space, such that the volume density decreases 
in geometrical progression as the distance from the kathode 
increases in arithmetical progression "f. 

In such circumstances, the kathode rays in their progress away 
from the kathode will acquire a high velocity in the initial stages 
of their motion, and subsequently will be affected but little by the 
weaker electrostatic fields which they traverse. 

Consider the rays from the opposed faces of the two kathodes 
in our experiment. The rays from each must in due course enter 

* Schuster, Proc. Roy. Soc. xlvii. p. 526, 1890. 

t J. J. Thomson, Conduction through Gases, 2nd ed. p. 541. 

230 Mr Orange, On certain phenomena of the kathode region. 

the dark space of the other. The particles will lose kinetic 
energy as they approach the second kathode, most of the loss 
occurring very near the latter owing to the character of the field, 
and they will tend to drift a little in the direction parallel to the 
kathodes. They will not quite reach the second kathode since 
they must have lost some energy by ionization en route ; they 
may subsequently travel back towards the kathode of origin and 
continue to swing across the interkathodic space, but always 
trending laterally outwards. Finally, they will have travelled to 
the right or left considerably and when their velocity is a minimum, 
i.e. when near one of the kathodes, they will be borne out of the 
interspace in a manner determined by the electrostatic field. 

As was stated above, the visible paths of the pencils indicate 
the presence of free negative charge in the middle of the inter- 
space, a view which can be supported as follows : 

For two reasons there is much ionization (and hence lumin- 
osity) in the interspace. 

(1) The kathode rays are not as swift here as elsewhere 
(since they start in the weaker field evidenced by the thickness of 
the dark space), and 

(2) the kathode rays, and also some proportion of the 
negative ions to which they give rise, oscillate about the median 
plane, so that at any instant there is an exceptionally large amount 
of ionization proceeding. 

The concentration of negative ions must be high in the neigh- 
bourhood of the median plane and many of them doubtless travel 
out along that plane and constitute the horizontal sheet of rays 
seen in the photographs. 

In summary then : 

We regard the electrostatic field as being due mainly to three 

(1) The actual charge on the kathodes ; the effect of this 
cannot be great, since the covered supports of the kathodes produce 
little or no visible effect. 

(2) The distribution of positive charge so that it is 
especially abundant very near to the surfaces of the kathodes, as 
assumed from Schuster's experiments, {loc. cit.) 

(3) An accumulation of negative charge about the median 
plane of the interspace. This must be postulated, I think, to 
account for the considerable divergence of the oblique ray sheets 
and their peculiar curvature. 

The oblique sheets are regarded as the kathode rays arising 
primarily from the kathodic interfaces and losing energy by 
ionization of the gas as they travel backwards and forwards 
between the kathodes. As long as the particles, in their surgings. 

Mr Orange, On certain phenomena of the kathode region. 231 

arrive within close range of the kathodes, they will reverse their 
paths in such a powerful field that they will gain sufficient impetus 
to travel in a fairly direct line towards the other kathode. When 
they have lost so much energy that they fail to reach the high 
intensity zone at the end of one of their oscillations, they will be 
dominated much more by the influence of the postulated region 
of negative charge at the centre of the system, and will be repelled 
out to form the oblique sheets. 

The ditference between the sheets at the higher and lower 
pressures can be explained simply thus : At the stage shown in 
Fig. 1, PI. VII, the kathode rays produced at the interfaces will 
lose much energy in crossing over (because of the higher gas 
pressure chiefly). 

Consequently the rays when they start out laterally will be at 
various distances from the kathode ; that is, they will have lost 
very different amounts of energy, according to the number of 
times they have crossed over. There will, however, be a minimum 
of energy lost corresponding to the case of a single traverse. 
The sharply defined boundary of the oblique ray sheets can be 
taken as the expression of this minimum. The other boundary of 
the rays is at this stage scarcely marked at all, owing to the 
indefinite range of possible energy losses of the particles in their 
preliminary movements. Probably, also, the spreading of the rays 
is conditioned partly by the great range of intensity of field as 
we cross the narrow Crookes' dark space. 

At lower pressures (e.g. Fig, 5, PI. VII), the particles will lose 
little energy in their surgings, and so when finally ejected they 
form a confined sheet. The large dark spaces characteristic of 
these lower pressures are associated with more uniform fields ; 
this also will be favourable to the production of confined sheets 
of rays. 

To test these views of the phenomena a few experiments were 
made with the two kathodes at different potentials. This was 
attained by having the lower plate connected as before to the coil 
terminal, while the upper plate was connected to it through a 
considerable electrolytic resistance. [The photographs obtained 
are unfortunately slightly out of focus (except Figs. 1 and 3, 
PI. IX), but they are clear enough to show the points referred to.] 
The series, Figs. 1 to 5, PI. IX, shows various combinations of 
potentials and pressures. In Fig. 1 the upper plate was quite 
disconnected externally. In the other cases it was connected 
through various amounts of resistance. 

The first thing noticeable is the inequality of the two Crookes' 
dark spaces, the upper one varying continuously with the potential 
and apparently vanishing when the plate is disconnected. This 

VOL, XV. PT. III. 16 

232 Mr Orange, On certain phenomena of the kathode region. 

seems to confirm the observations of Schuster* on the relation 
between the thickness of the dark space and the strength of the 

As regards the sheets of rays, the appearances in these experi- 
ments agree fairly well with the explanations advanced above. 
In Fig. 1, PI. IX, the kathode rays from the lower plate strike the 
upper one violently. Some of the rays graze the edge of the 
plate and produce the sharp, nearly vertical shadow which may be 
noticed. The upper plate emits secondary kathode rays, which 
are not sufficiently powerful to travel far towards the lower plate, 
but are very soon thrown out sideways as three highly luminous, 
but ill-defined sheets, corresponding to the three sides of the 

In Figs. 2 and 4, PI. IX, the form of the lower ray sheet is clear 
and it will be noticed that in these cases it is much further away 
from the kathode than in any of the examples on Pis. VII and VIII. 
This is probably due to the fact that rays from the upper (low 
potential) plate will not have sufficient energy to approach near to 
the lower kathode and hence when they finally start moving side- 
ways they are at a considerable distance from it. No such feature 
is associated with the upper plate. The rays starting from near 
the latter form two distinct beams (two on each side that is) 
in most of these examples, (e.g. Figs. 2 and 4, PI. IX.) 

These two beams might be explained as being due to 

(i) the primary rays from the upper plate which have 
travelled back after visiting the neighbourhood of the lower 
one, and 

(ii) the secondary rays from the upper plate due to the 
impact of the primary rays from the lower one. 

The change which has occurred in the position and direction 
of the " median " beams, owing to the alteration of the potential 
of the upper plate, is quite what one would anticipate. (Fig. 2, 
PI. IX.) 

In conclusion, I wish to thank Prof. Sir J. J, Thomson for his 
valuable suggestions and kindly interest in these investigations. 

My gratitude is due also to Mr E. Everett for his ready 
assistance at various times. 

* Schuster, loc. cit. p. 556. 

Phil. Soc. Proc. xv., Pt in. 

Plate IV. 

Pliil. Soc. Proc. XV., Pt III. 

Plate V. 


PhM. SoG. Proc. XV., Pt III. 

Plate VI, 



Phil. SoG. ProG. XV., Pt III. 

Plate VII. 






Phil. Soc. Proc. xv., Pt iii. 

Plate VIII. 








Phil. >Soc. Proc. XV., Pt m. 

Plate IX. 

Ki- 1 

Fig. 2 

Fig. 4 

Fiir. 3 


FiK. 6 

P. 233, line 10 from top, for species read examples. 

Mr Harding, Note on two new Leeches from Ceylon. 233 

Note on two new Leeches from Ceylon. By W. A. Harding, 
M.A., Peterhouse, 

[Read 3 May 1909.] 

The leeches here described were collected in Ceylon by Miss 
Muriel Robertson, who very kindly seat them to me for examina- 
tion, together with information respecting their habits and the 
hosts upon which they were found. 

The material placed at my disposal was not in a condition 
very favourable for the examination of external features. It 
comprised examples of two species hitherto unrecorded, of which 
a brief description is given below. 

1. Ozohranchus shipleyi, no v. sp. 

Eleven species, fixed in corrosive sublimate and preserved in 
alcohol, were examined. The largest specimen was 5 mm. in 
length ; this species therefore is one of the smallest of known 

Body depressed, divided into two distinct regions and generally 
resembling Branchellion in form. Complete somite formed of 
three rings. Abdominal region of the body provided with eleven 
pairs of digitate branchiae, the posterior smaller and less branched 
than the anterior pairs. 

Anterior sucker not distinct from the bod3^ Acetabulum 
cupuliform, shallow, centrally-attached and very large, its diameter 
being equal to nearly one-third of the total length of the animal. 

Eyes two (?). 

Habitat :— Fresh-water ; parasitic on the Ceylon terrapin, 
Nicoria trijuga. 

I have associated with this species the name of Mr A. E. 
Shipley, to whom T am indebted for much kind help and advice. 

2. (rlossiphonia ceylanica, nov. sp. 

The species is founded upon one specimen preserved in 
alcohol. This had assumed a brown colour, somewhat lighter 
upon the ventral surface. Irregular, black, median and marginal 
patches and traces of four longitudinal brown stripes were seen on 
the dorsal surface. 

Head distinct from the much depressed and slender body. 
Six eyes arranged in two sub-parallel rows, the first pair ap- 


234 Mr Harding, Note on two new Leeches from Ceylon. 

Counting the first oculiferous ring as the first ring, the eyes 
occur on the first, second and fourth rings ; the male genital 
opening lies between the 26th and 27th rings and the female 
opening between the 29th and SOth rings (?) ; the anus lies 
between the 68th and the 69th (and last) ring; and rings %Q, 67 
and 68 are partly double. 

Length, in alcohol, about 7f mm. 

Habitat : — Ceylon, in fresh-water ; parasitic on the soft-tortoise, 
Emyda vittata. 

Mr Sinclair^ Note on abnormal pair of appendages, etc. 235 

Note on the abnorrtial pair of appendages in Lithobius. 
By F. G. Sinclair, M.A., Trinity College. 

[Received 3 June 1909.] 

The presence of an abnormal extra pair of appendages is of 
interest to me, as I have examined a great number of abnormalities 
in the Mj'riapoda, but I am inclined to give a different inter- 
pretation to the facts from that given in the note referred to by 
Doncaster*, in which the appendage is taken to be a reduplication 
of the poison claw. 

The abnormalities which are very frequent in Myriapods fall, 
in all cases that are familiar to me, into two classes. A re- 
duplication in the transverse axis of the body or appendage, or a 
reduplication in the longitudinal axis of the body or appendage. 
The former is the more frequent — an example being a reduplication 
of part of the antenna or leg forming a bifurcation. 

The description of the small processes described as teeth, 
jointed to the base of the appendage and the drawing of them, 
remind me strongly of two small processes which are commonly 
present on the end of the larval appendages in Myriapods. They 
are moveable by muscular fibres, and, as the animal grows up, one 
of them usually degenerates and disappears while the other changes 
to a claw or spike. 

In the reduplication of a part in the longitudinal axis I should 
think it more likely that the abnormal part would be posterior to 
that of which it was a copy, following the order in which the 
normal segments are formed. 

It results from these considerations that I take the abnormal 
appendage described in the note to be a reduplication, not of the 
poison claw, but of the second maxilla. The basal joint with the two 
small processes I believe to be an imperfectly formed transverse 
reduplication of the other branch, so that if the development 
had gone a step further there would have been two similar 
branches on either side. 

According to my view the undivided plate at the base would 
be — not the coalesced basal joints of the poison claws, but a 
metamorphosed sternal plate. 

Of course if a poison gland and duct had been found present 
it would have upset this view, but that does not seem to have 
been the case. It is worth remembering that in the Myriapoda 
portions of proliferous tissue from which complete segments are 
formed normally are present till comparatively late in life. The 
complete number of segments in Diplopoda is not present for 
a long period. 

* Proe. Camb. Phil. Soc. xv. p. 178. 

236 Mr Thomas, On a specwien of the cone 

On a specimen of the cone Calamostachys biune3^aua (Garr.). 
By H. Hamshaw Thomas, B.A., Downing College. [Communicated 
by Mr E. A. Newell Arber.] 

[Bead 3 May 1909.] 

Forty years have now elapsed since the first description of the 
cone Calamostachys hinneyana was published*, but hitherto no 
petrified specimen has been found showing its connection with 
vegetative organs of any kind. 

In December last, I received a specimen of a cone with four 
whorls of Calamite leaves attached to the base, derived from the 
Halifax Hard Bed at Huddersfield. The cone was at least 14 mm. 
long and about 5 mm. broad. It was cylindrical in shape and 
eight whorls of sporangiophores are preserved. 

The structure of the cone agrees closely with that of specimens 
previously described f, and the axis and sporangiophores do not 
present any unusual features. Several of the bracts are very well 
preserved and show some new points of interest. As usual, they 
are coherent at the base to a disc, and, on becoming free, turn 
sharply upwards. Each is provided with a vascular bundle, the 
centre of which is occupied by a group of very small xylem 
tracheides surrounded on all sides by small thin-walled cells, 
probably phloem. The bundle may possibly therefore be con- 
centric in structure and not collateral as formerly supposed, though 
it is very difficult to arrive at any certain conclusion. The free 
portion of the bract bears a striking resemblance to a leaf. It 
consists largely of sclerenchymatous fibres on the adaxial side, 
while a layer of rudimentary pallisade tissue forms the other side. 
The small bundle occurs in the centre of the bract, and on the 
inner side of the pallisade tissue, a zone of cells with dense black 
contents is found. There is a thin epidermis on the outside. 

At the base of the cone, there is a whorl of bracts resembling 
the leaves still more closely. Immediately below this we have a 
whorl of appendages differing completely from the leaves, bractS; 
and sporangiophores, and seen in longitudinal section as a broad 

* Carruthers, W. " On tlie fruit spike of Calamites." Journal of Botany, 
vol. V. 1867. 

t Bmney, E. W. "Observations on the Structure of Fossil Plants." Mem. 
Palaontographical Soc. p. 24. 1868. Williamson, .W. C. " On the organisation 
of the Fossil Plants of the Coal measures," Parts iv. x. xi. xv. Phil. Trans. 1873, 
1880, 1881, 1889. Hick, T. " On Calamostachy.'; binneyana." Proc. Yorks. Geol. 
and Polyt. Soc. vol. xii. pt. iv. 1893. Williamson, W. C. and Scott, D. H. 
" Further Observations on the organisation," etc. Phil. Trans. 1894. 

Calamostachys binneyana (Garr.). 237 

ring of parenchymatous tissue. This may be compared with 
the annulus of the cones of modern Equisetums. It contains 
however some rudiments of vascular tissue. The discovery of 
this organ further illustrates the similarity between the Palaeozoic 
Calamites and modern Equisetaceae. 

Below the " annulus " there are four whorls of foliage leaves. 
These are small linear, rather falcate structures, about 3 mm. 
long, less than 1 ram. broad, and free at the base. They are 
almost identical in their size, form, and arrangement, with those 
known from impressions as Galamocladus grandis (Sternberg). 
The structure of the leaves differs somewhat from those which 
have been already described*. The upper portion consists of 
a large strand of sclerenchymatous fibres running the whole 
length of the leaf but smaller than that occurring in the bracts. 
A small bundle occupies the centre of the leaf, and below, there 
is a band of cells with dense black contents. The latter is 
crescentic in transverse section and separates the pallisade tissue 
from the bundle and fibres; its function is not yet certain. The 
pallisade tissue is greater in amount than in the bracts, and 
consists of radially elongated cells with thin walls and numerous 
intercellular spaces. On its outside, there is a narrow epidermis. 
Stomata are seen in some places, and were probably slightly sunk 
below the surface of the leaf. 

The internodes of the stems between the leaf whorls seem to 
have been covered with small hairs, which also occur on the 
lower part of the cone. They are preserved as small, dense, 
black bodies, and may perhaps have been glandular. 

The form of the cone and leaves shows that it is probably 
identical with the impressions named by Weiss f Paracalamostachys 
williamsoni, and also with Zeiller's Calamostachys grandis l- It 
seems possible that the name Calamostachys binneyana should be 
applied as indicating a type of structure rather than a species, and 
hence the name Calamostachys grandis is perhaps the best desig- 
nation for the cone described here. 

The discovery of this specimen is of interest for several 
reasons. It furnishes for the first time direct evidence that this 
well-known cone was borne on a Calamite plant. The question of 
its affinities — at one time debated with keenness — was practically 
settled some years ago, but the stem and leaves of the plant have 

* Hick, T. " On the structure of the leaves of Calamites." Mem. and Proc. 
Manchester Lit. and Phil. Soc. vol. ix. p. 179. 1895. 

t Weiss, C. E. " Steinkohlen-Calamarien II." Abhandlungen zur geologischeii 
Specialkarte von Preussen, Band v. p. 193. 1881. 

J Zeiller, R. Flore fossile du bassin houiller de Valenciennes, p. 376. PL 59, 
Figs. 4—7. Paris, 1886. 

288 Mr Thomas, On a specimen of the cone, etc. 

hitherto remained unknown. The leaves have now been dis- 
covered, and there is little doubt that, before long, a petrified 
stem bearing leaves of this kind will be found. The " annulus " 
and the hairs on the stem are here described for the first time. 

The great similarity of structure between the foliage leaves 
and the bracts of the cone is also a point of some interest, as 
indicating the foliar nature of the latter. This, together with 
the probable occurrence of an annulus in Calamostachys, is of 
some importance in the discussion of the morphology of the cones 
of the Equisetales. 

My best thanks are due to Mr Arber for his kind advice and 
assistance in this work. 

Mr Gregory, Note on the Histology of the Giant, etc. 239 

Note on the Histology of the Giant and Ordinary Forms of 
Primula sinensis. By K P. Gregory, M.A., St John's College. 

[Head 17 May 1909.] 

(Plate X.) 

During the last few years the Giant form of Primula sinensis 
has become well established in cultivation, and is now known in 
many of the numerous horticultural varieties of this genus. 
Nothing definite is known as to the origin of the form, nor can 
we at present say anything as to the behaviour of the Giant and 
Ordinary characters in cross-breeding, although experiments are 
now in progress in this connexion. 

Flowers of the two plants described. In each case the upper flower is newly 
opened, the lower is older. Scale divided in inches. From a photograph. 

Plants of the Giant form are of a somewhat coarser general 
habit than those of the usual form. As compared with the latter, 
they are characterized by the stoutness of their stems and petioles, 
and by their larger leaves and flowers. In Giants of the " Stellata " 
type, the petal-lobes are broad, and, unlike those of the ordinary 
form, overlap one another to a greater or less degree (see text 
figure). My experience of the seeds of the Giant form is limited 
to those obtained this year from a few plants ; they were, on the 
average, larger than those of the ordinary type. I am indebted 

240 Mr Gregory, Note on the Histology of the Oiant 

to Mr Leonard Sutton for further information on this point ; he 
writes: "With regard to the size of the seeds, we do not find 
much difference in the Stellata forms, but in the Florist's type, 
seed of the Giant varieties, though variable from year to year, is 
always larger and flatter than that of the smaller flowered sorts." 

At Professor Bateson's suggestion I have made observations 
with a view to comparing the nuclei of the two forms. The 
plants chosen for the purpose were (1) a Giant White Star with 
dark red stems, and (2) a White Star of the ordinary habit, but 
closely resembling the Giant in all other characters. For both of 
these plants I am indebted to Messrs Sutton of Reading. 

The primary object of the investigation was to discover whether 
there might be a difference in the number of the chromosomes in 
the two forms, an idea suggested by the results of Miss Lutz* and 
Gatesf in Oenothera gigas. Upon this point the answer is definitely 
in the negative; the number of the chromosomes is the same in 
both forms oi Primula sinensis, viz. 12 (reduced) and 24 (somatic). 
The reduced number of chromosomes is shown with quite diagram- 
matic clearness in sections transverse to the spindle at metaphase 
or anaphase of either of the two meiotic divisions (figs. 1 and 2). 
In the somatic divisions the chromosomes are more closely crowded 
and their precise number is less easy of determination; but several 
counts have given numbers ranging from 22 to 24, and there can 
be no doubt, I think, that the number may be correctly stated at 
24. I have no evidence which suggests that there is any tendency 
to variation in the number of chromosomes which occur in the 
somatic mitoses found in various regions of the floral organs. 

But although the two forms are alike in the number and form 
of the chromosomes, they give very distinctly the impression that 
a difference exists between them in the size of the chromosomes 
(at any rate as they appear at metaphase of the heterotype 
division), in the size of the resting nuclei, and correspondingly in 
the size of entire cells. 

In testing this point the comparison between the two forms 
was made by means of figures drawn to exactly the same scale 
with the help of a camera lucida, and by measuring the resting 
nuclei with an ocular micrometer, the measurements being taken 
along, and at right angles to, the long axis of such nuclei as were 
not circular in outline. The drawings and measurements were made 
upon material which had been carefully fixed, and showed little or 
no signs of shrinkage during the process. The material was cut 
in paraffin into sections sufficiently thick to contain entire nuclei 
Avhich had been untouched by the knife of the microtome. In a 

* "A Preliminary Note on the Chromosomes of Oenothera Lamarckiana and 
one of its Mutants, 0. gigas." Science, N. S. 26, p. 151, 1907. 

t "The Chromosomes of Oenothera." Ibid. N. S. 27, p. 193, 1908. 

and Ordinary Forms of Primula sinensis. 241 

few test cases the vertical measure of the nucleus was estimated 
by focussing on to the upper and lower walls of the nucleus by 
means of the micrometer fine adjustment, taking the mean of 
three readings. In each of these cases the measure so obtained 
approximated very closely to those taken in the horizontal plane. 
It is of course desirable that the tissues selected for com- 
parison should be composed of cells which approach, as nearly as 
may be, to uniformity of shape and size. Such tissues are to be 
found in various epithelial layers, notably in the very regular 
layer of cells which surrounds the embryo sac in the mature 
unfertilized ovule. This layer is the " couche de revetement " of 
Warming* and Vesquef, and the "tapetura" of Billings j, all of 
whom have recorded its existence in species of Primula. Other 
layers whose nuclei have been compared are the epidermis of the 
young stigma as seen in approximately median longitudinal section, 
and the epithelia of the young developing ovules. Equally favour- 
able for purposes of comparison are the nuclei of the pollen mother 
cells, since the individual cells at the same stage of development 
are remarkably uniform in size, and the stages are marked by 
easily recognizable characters of the nucleus, so that a just com- 
parison can be made. I hoped to test the matter further by 
measurements of the cells of the young embryos as they developed 
within the seed, but owing to the resistance offered by the thicken- 
ing integuments to the penetration of the fixing fluids I was unable 
to obtain sufiiciently good material. The apex of the young 
radicle may perhaps allow a further test, when it becomes available 
later in the season. 

In dealing with the size of the chromosomes of the two forms, 
I have had to be content with a comparison of the drawings made 
with a camera lucida, since the chromosomes are too small to be 
measured with any degree of accuracy by means of an ocular 
micrometer. Figs. 1 and 2 show the groups of chromosomes of 
the Ordinary and Giant forms, respectively, as they appear at 
metaphase of the heterotype division. The figures represent the 
view transverse to the spindle; the outlines of the chromosomes 
were carefully drawn, and I think the difference between the two 
is not exaggerated. Spindles seen in longitudinal view show that 
the two forms had reached as nearly as possible identical stages; 
a similar slight difference in the size of the chromosomes of the 
two forms is apparent also in these longitudinal views. In the 
somatic mitoses which I have seen the chromosomes were too 
crowded to permit of fair comparison. 

* " De I'Ovule." Ann. des Sci. Nat., Ser. vi. Tome 5, p. 235, 1878. 
t " Sur le Developpement du Sac embryonnaire." Ibid., Ser. vi. Tome 8, p. 360, 

J "Beitrage z. Kenntniss d. Samenentwickelung." Flora, 88, p. 277, 1901. 

242 Mr Gregory, Note on the Histology of the Giant, etc. 

I give in the table (p. 243) some measurements taken from 
edge to edge of the group of chi'omosomes in the equatorial plane 
of the heterotype division, but any difference in size thus indi- 
cated is perhaps not very trustworthy, since it is slight and its 
measurement depends entirely on reading by the eye to fractions 
of the micrometer scale. 

But in the nuclei of the pollen mother cells and in the resting 
nuclei of the various epithelial layers the differences indicated by 
a comparison of the camera drawings are clearly borne out by a 
comparison of the measurements (see table), all of which show the 
same result, namely, that the nuclei of the Giant plant are, on the 
average, larger than those of ordinary form, in the proportion of 
from 4 to 10°/^ of each diameter. In the case of the developing 
pollen mother cells great care was taken in choosing exactly com- 
parable stages, though, as a matter of fact, there appears to be 
only slight change in size when the cells have reached the stages 
under consideration. Figs. 3 and 4 represent the stage whose 
measures are recorded under the head " Prophase, with looped 
thread"; figs. 5 and 6 represent those recorded under the head 
" Prophase, diakinesis." The nuclei selected for measurement were 
chosen at random, with the provision that any nuclei that showed 
any signs of shrinkage or distortion during fixation, or were cut 
by the knife, were excluded. In making the measurements the 
divisions of the micrometer scale were read to fifths by the eye ; 
to this extent therefore the measurements are only approximate, 
but the preponderance of the measurements obtained for the 
Giant over those obtained for the ordinary form, in the average 
of a number of measurements, although not great, is, I think, too 
consistent and regular to be accounted for by experimental error. 

Perhaps the clearest evidence is to be obtained from an 
examination of the columnar cells of the ovule, to which reference 
has already been made. Both in the measurements and in the 
drawings these show a very consistent difference in size. Fig. 7 
represents nuclei from this layer, the upper row being those of the 
Giant, the lower row those of the ordinary form. It will be 
noticed that the third and fifth are the largest nuclei in the 
lower row; they are almost exactly equal in size to the first and 
fourth of the upper row, which are, to say the least, distinctly not 
the largest of that row. In the ordinary form some care was 
exercised in the selection of the nuclei to be drawn, lest any 
difference might be unintentionally exaggerated. The nuclei 
shown in the figure were afterwards measured ; the average of 
the measures of the six nuclei of the ordinary form was found to be 
3*7 X 3*4 scale divisions, while the average in the case of the six 
nuclei of the Giant was 3"9 x 3*7. If these figures are compared 
with those given in the table, it will be seen that the difference is, 
if anything, diminished rather than exaggerated in the figure. 

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244 Ml' Gregory, Note on the Histology of the Giant 

As a further test drawings were made of the six largest nuclei 
to be found in this layer in one section passing through the ovule 
in an approximately median plane. The result is shown m 
fig. 8, in which the left hand row represents nuclei of the 
ordinary form, the right hand row nuclei of the Giant. The 
difference here is obvious. Lest chance should have favoured the 
Giant, further drawings were made of the ordinary form, choosmg 
the largest nuclei which could be found in the serial sections of 
some four or five ovules which were mounted on the same slide. 
The six largest of these are reproduced in fig. 9; it will be noticed 
that they are rather smaller than the six nuclei drawn from one 
section of one ovule of the Giant form. 

Evidence has been given above which I think clearly suggests 
the existence of a difference in size between the nuclei of the 
Giant and ordinary forms. It remains to compare the size of 
entire cells. It is very desirable that in instituting this com- 
parison measurements should be made of the living pollen mother 
cells and living pollen grains, but at the time when material of 
this kind was available the trend which this work has since taken 
was unforeseen. Microtome sections of growing tissues are, at the 
best, unfavourable for making measurements of entire cells, and in 
default of measurements of isolated cells such as might be pro- 
vided by the pollen, I have had recourse to hand sections of the 
living tissues of the stems and petioles. Transverse sections were 
cut from the living material and mounted in water, so that no 
disturbance due to shrinkage was possible. Care was taken to 
avoid any disturbance due to the drag of the razor m cutting. 
Measurements of the diameters taken when the sections were cut 
show that the stems and petioles of the Giant are thicker than 
those of the ordinary form, the proportional diflference being about 
4 to 127 of the diameters, or of the same order of difference as 
that found in the size of the nuclei. The size of the individual 
cells encountered in such sections is naturally very divergent, but 
by drawing the outlines of the cells to exactly the same scale 
the difference in their size in the two forms is strikingly shown. 
A number of drawings were made in this way from sections ot 
various comparable regions of the stems and petioles. Two pairs 
of these drawings are shown in figs. 10 and 11, and 12 and 13. 
The figures represent sections, chosen at random from a number 
floating in a watch glass, of the main flowering stems of the two 
forms, in each case taken half way between the base of the stem 
and the lowest umbel of flowers; figs. 10 and 11 show the region 
of the pith, and figs. 12 and 13 the cortical region, m the ordinary 
and Giant respectively. It will be noticed— what has been found 
to be the case in all the sections made— that the cells of the Giant 

and Ordinary Forms of Primula sinensis. 245 

are, cell for cell, larger than those of the ordinary form, and that 
to a degree sufficient in itself, I think, to account for the greater 
thickness of the Giant. Just the same resemblance in structure 
and difference in size is found in other regions of the stem and in 
the petioles of the leaves ; the difference is sufficiently illustrated 
in the figures of the stem, and I have not thought it necessary to 
multiply the number of figures in order to illustrate the petioles. 
In these observations there is, I think, strong ground for the 
suggestion that the difference between the Giant and ordinary 
forms may be referred to a difference in the size of the cells ; 
that is, the character of Giantness manifests itself in the cells 
themselves and not merely in the plant as a whole. At present 
only a suggestion can be made, for we are as yet ignorant as to the 
extent to which individual variations among plants of the same 
type may affect these results ; my observations have been limited, 
for want of others, to one pair of plants. I hope in the future to 
make a comparison between a number of Giant and ordinary 
plants, grown, as were the pair described here, under similar 


The figures were all drawn with a Camera lucida. Figs. 1 — 6, 8, 
and 9 were drawn with a Zeiss 2 mm. Apochromatic Obj., 18 Ocular. 
For fig. 7 the same objective with Ocular 8 was used. Figs. 10 — 13 
were drawn with a f in. objective. 

Fig. 1. Ordinary form; metaphase of the heterotype division in 
the pollen mothei cell, the section being transverse to the spindle. 
X about 3200. 

Fig. 2. Giant form; as fig. 1. 

Fig. 3. Ordinary form ; prophase of the heterotype division of the 
pollen mother cell, x 3200. 

Fig. 4. Giant form ; as fig. 3. 

Fig. 5. Ordinary form ; later prophase (diakinesis) of the hetero- 
type division, the chromosomes in the form of gemini. x 3200. 

Fig. 6. Giant form ; as fig. 5. 

Fig. 7. Nuclei from the layer of cells surrounding the embryo sac ; 
the upper row from the Giant, the lower row from the Ordinary form. 
X 1420. 

Fig. 8. Nuclei from the same layer ; the left hand row from the 
Ordinary form, the right hand row from the Giant form. The nuclei 
shown were the largest to be found in one section of an ovule in each 
case. X 3200. 

246 i/r Grego7^y, Note on the Histology of the Giant, etc. 

Fig. 9. Nuclei from the same layer. The nuclei shown were the 
six largest to be found in the serial sections of four or five ovules of the 
Ordinary form, x 3200. 

Fig. 10. Pith cells and primary xylem from a T. S. of the flowering- 
stem of the Ordinary form, x 210. 

Fig. 11. The same in the Giant form, x 210. 

Fig. 12. Cortical cells from a T. S. of the flowering-stem of the 
Ordinary form, x 210. 

Fig. 13. The same in the Giant form, x 210. 

Phil. Soc. Proc, xv., Pt in. 




Plate X. 






Mr Purvis, The influence of dilution on the colour, etc. 247 

Tfie influence of dilution on the colour and the absorption 
spectra of various permanganates. By J. E. Purvis, M.A., 
St John's College. 

[Read 17 May 1909.] 
[Plate XI.] 

It has always been considered that permanganate solutions 
show similar absorption bands whatever be the nature of the 
element or group of elements acting as the positive ion. Ostwald's 
experiments * comparing the absorption spectra of the solutions 
of a number of permanganates, whereby there appeared to be no 
change either in the position or the width or the intensity of the 
bands, appeared to prove conclusively that such absorptions were 
independent of the nature of the positive ion. The only criticism 
which could be brought against the experiments was, and is, that 
sufficient dispersion of light had not been used. It is probable 
that any changes would be exceedingly small, and in order to 
distinguish small differences, if there are any, it would seem 
to be desirable to use a greater dispersion than was used by 

It is also well known that dilute solutions of permanganates 
gradually change their colours when they are kept for some time, 
and it is usual to explain such changes by the action of light. 
The change is only noticed in very dilute solutions, and, ordinarily, 
a brown colour is produced. No observations are recorded with 
regard to changes in the absorption bands during the colour 
changes ; nor are there any observations to indicate that the 
changes take place in the dark, or out of contact with the air. 
The following description gives some account of experiments 
conducted in these directions. 

Experimental part. 

The separate bands of solutions of permanganates can only be 
seen when the solutions are very dilute : and, after some preliminary 
trials, the following standard solutions of the permanganates of 
barium, zinc and potassium were made : 

0"37.5 gram barium permanganate dissolved in 1000 c.c. distilled 

0'262 gram zinc permanganate dissolved in 1000 c.c. distilled 

0"316 gram potassium permanganate dissolved in 1000 c.c. 
distilled water. 

Three separate solutions of each salt were investigated, and 

* Zeits.physik. Ghem. Vol. ix. (1892), p. 579. 

VOL. XV. PT. III. 17 

248 Mr Purris, The injiuence of dilution on the colour 

each solution contained the same amount of permanganate. The 
solutions were placed in their respective cells or troughs, one of 
which was 5 mm. long, a second one was lo4 mm. long, and a 
thiixi one was 810 mm. long. The comparative solutions were, 
therefore, made by diluting the strongest tme o0"8 and &2 times 

The apparatus used in these experiments has been previously 
described* by the author in some experiments on the absorption 
spectra of solutions of various salts of didymium and erbium. The 
source of light was a Welsbach burner without the glass, whose 
rays passed through a small circular aperture and thence carried 
through the solutions by a quartz lens ; and the emerging light 
was focussed on the slit of the spectroscope. The times of exposure 
vaiied from 1, 3 and 5 minutes: but the same length of time was 
allowed for each series of comparative observations. In order 
to make the comparison as strict as possible, blank tubes con- 
taining distilled water and of exactly the same lengths and 
diameters as those containing the solutions were placed in front 
of the slit when photographs were taken of the stronger solutions 
contained in the 5 mm. cell. By this arrangement, the light mys 
passed through the same thickness of water. 

In the preliminary series of observations photographs were 
taken immediately after the solutions were made ; and although 
there appeared to be no ditierence in the colour of the solutions, 
there were ditierences in the width of the bands as well as in the 
amount of general absorption of light in the more refrangible 
parts of the spectrum. After the solutions had stood for some 
houi-s changes in the colour of the dilute solutions were also 
observed. Fresh solutions of the permanganates oi barium and 
potassium were then made, and they were allowed to stand two 
days when photographs of the absorption spectra and changes in 
the colour were noticed. 

The following notes describe these observations ; and in order 
to shorten the description it should be stated that the phrases 
"5 solution," '' 154 solution," and '"olO solution" mean that there 
was the same amount of permanganate in the tubes whose lengths 
were 5 mm., 154 mm., and 810 mm. respectively. 

The bauds observed were \\ 570, 546, 524, 504, 4SGf, and 
they are numbered in the following notes so that 

X 570 = 1, 

546 = 2, 

524 = 3, 

504 - 4, 

486 = 5. 

* Proe. Camb. Phil. Soc. Vol. xii. pt. iii. p. 200. 
t Leeoq de Boisbaudrau, Spectres hn)nneu.r, p. 109. 

and the absorption spectra, of various permanganates. 249 

The other bands were too faint to make any exact observations of 



tSolutions of the permanganates of barium and potassium 

were made and allowed to stand for two days in the full glare 

of a well lighted room. They were then examined; and the 

5 solutions showed the well known permanganate tint ; whilst the 

154 solutions were pink, and the 310 solutions were yellowish 


A. Barium permanganate l ,r-^ i 4.- 
■p, , . ' ] ° ^154 solutions, 

rotassium do. J 

do. do. 5 solutions. 

Band 1 was narrower in the 154 solutions than in the 
5 solutions ; band 2 was also narrower, and the differences were 
well marked ; band 3 was also narrower but the difference was 
not so marked as in band 2, whilst bands 4 and 5 were a little 
wider in the 154 solutions than in the 5 solutions. Also the 
general absoi-ption was much greater in the 154 solutions; and the 
position of the bands in the 5 solutions was more towards the red 
end of the spectrum than in the 154 solutions. 

Barium permanganate "1 o,^ , ,. 

Potassium do. J ' 

do. do. 5 solutions. 

Bands 1, 2 and 3 were narrower in the 310 solutions, and 
these differences were more marked than in the corresponding 
bands of the 154 solutions ; and the bands 4 and 5 were also much 
wider than the corresponding bands of the 5 and 154 solutions. 
Also the general absorption had greatly increased, and it was 
greater in the 310 solutions than in the 154 solutions. The 
position of the bands in the 5 solutions was also more towards 
the red end of the spectrum : the difference in this respect was 
more marked when compared with the 810 solutions than with the 
154 solutions. 

B. The solutions were allowed to stand two days longer 
and they were again examined. In the 154 solutions the general 
phenomena were very like those observed before, except that 
the general absorption had slightly increased. In the 310 
solutions the general absorption had also slightly increased, and 
the differences in the width of the bands 2 and 3 were much more 

C. The solutions then stood for three weeks and they were 
again examined. The 154 s(jlution of barium permanganate was 
a reddish brown colour ; the bands 1, 2 and 3 were much narrower 
than the corresponding bands in the 5 solution, and the bands 


250 3Ir Purvis, The influence of dilution on the colour 

4 and 5 were wider than those in the 5 solution. The general 
absorption was more marked in the 154 sokition than in the 

5 solution. The 154 solution of barium permanganate showed 
that the bands 1, 2 and 3 had also become narrower, and the 
bands 4 and 5 were wider; but the general absorption had not 
altered much from the previous observation. The 310 solution 
of barium permanganate was of a light brownish yellow colour 
and perfectly clear. The 5 solution showed the five bands well 
marked ; and the 310 solution showed that the bands 1, 2 and 3 
had almost disappeared, whilst the bands 4 and 5 had quite 
disappeared and just beyond these there was complete general 

The colour of the 154 solution of potassium permanganate 
was brown, and the solution was quite clear. The bands 1, 2 and 
3 were much narrower than the corresponding bands in the 
5 solution, whilst the bands 4 and 5 were a shade wider, and 
just beyond band 5 there was complete general absorption ; 
whereas there was little or no difference in the colour or the 
general absorption in the 5 solution. In the 310 solution of 
potassium permanganate the bands 1, 2 and 3 were only just 
visible ; bands 4 and 5 had completely disappeared, and there was 
complete general absorption just beyond; whilst in the 5 solution 
the bands were just as before, and there was no apparent change 
in the general absorption. 

The general results of the above observations indicate a 
development of considerable differences in the more diluted 
solutions both as regards colour and absorption bands. The 
usual explanation is that light vibrations are the cause of such 
changes. In order to test this, similar solutions of the perman- 
ganates were made in the dark, and they stood covered up in 
a dark cupboard so that no light could enter. The solutions were 
examined after two days ; and the following notes describe the 


Solutions of permanganates of barium and potassium made in 
the dark and allowed to stand for two days well covered up and 
placed in a dark cupboard and then examined. 

The colours of the 154 solutions had changed from the well 
known permanganate tint to a pinkish colour ; and the colours of 
the 310 solutions had become a rose colour with a tinge of brown. 
The strong 5 solution did not appear to have changed. The 
absorption spectra of these solutions were also examined. 

D. Barium permanganate | ^^^ .^lutions. 
rotassmm do. J 

do. do. 5 solutions. 

and the absorption spectra of various permangoAiates. 251 

The change in colour was accompanied by some changes in 
the appearance of the absorption bands. There appeared to be 
little or no change in the band 1 ; band 2 was not so wide in the 
dilute solutions ; and similarly in band 3, although the difference 
was not so well marked as in band 2 ; whilst in bands 4 and 5 
there was little or no difference in the solutions. Besides 
alterations in the bands, there was much more general absorption 
in the 154 solutions. 

E. Barium permanganate "I ^i q i ^• 
Potassium do. / 

do. do. 5 solutions. 

Band 1 in the 310 solutions was a shade narrower than the 
corresponding band in the stronger solutions: the width of band 2 
was much less in the 310 solutions (cf. the 154 solutions): band 3 
had also decreased in width but the difference was not so marked 
as in band 2 ; band 4 was also very slightly decreased in width : 
whilst band 5 did not appear to have decreased, although there 
was a slight difference in the intensity. 

Also, there was much more general absorption in the 310 
solutions. Besides these changes, the position of the bands 1 
and 2, and in a less degree, band 3, is not so far towards the 
red end as in the 5 solution, and the same remark applies to 
bands 4 and 5 although the difference is not so marked. 

The above solutions stood two days longer in the dark, and 
they were again examined. 

The colours of the 154 solutions were of a rose red tint — they 
were not so brown as the solutions made two days earlier and 
kept in the light ; whilst the 310 solutions were yellow brown. 

G. Barium permanganate | ^^^ ^^^^^.^^^ 
rotassium do. J 

do. do. 5 solutions. 

There appeared to be little or no change in band 1 in all the 
solutions; band 2 was much narrower in the 154 solutions; 
band 3 in the 154 solutions was also narrower than in the 
5 solution, but the difference was not so marked as in band 2 ; 
bands 4 and 5 did not show a marked difference, although they 
appeared to be a shade wider in the 154 solutions. 

There was more general absorption in the 154 solutions, and it 
had increased a little since the observations of two days ago. 

H. Barium permanganate 1 q^ ^ , ,. 
Potassium do. J 

do. do. 5 solutions. 

Band 1 was not quite so wide in the 310 solutions as in the 

252 Mr Purvis, The influence of dilution on the colour 

5 solution ; band 2 had decreased in width very considerably 
in the 310 solutions ; band 3 was also not so wide in the 310 
solutions, but the difiference was not so striking as in band 2 ; 
and bands 4 and 5 have very slightly increased in width in the 
310 solutions. 

Besides these changes, there was more general absorption in 
the 310 solutions, but the increase since the observations of two 
days ago was not very great. 

Also, the shift of the bands towards the red end as noticed in 
E was similarly marked. 

J. The solutions stood for three weeks longer in the dark and 
they were again examined. 

Barium permanganate 1 , c ^ i j.- 
-T) , ■ ^ 1° ^ 154 solutions, 

rotassmm do. J 

do. do. 5 solutions. 

The 154 barium permanganate solution was of a purplish 
colour, and there was a slight opalescence ; the 154 potassium per- 
manganate solution was rose pink coloured and perfectly clear. 

In the 154 barium permanganate solution the bands 1, 2 and 
3 were again narrower than the corresponding bands in the 
5 solution ; whilst bands 4 and 5 were slightly wider, and general 
absorption was more pronounced in the 154 solutions than in 
the 5 solution. Similar remarks apply to the 154 potassium 
permanganate solution. 

K. Barium permanganate | ^i a i j.- 
Potassium do. J 

do. do. 5 solutions. 

These solutions were perfectly clear, and showed no opalescence. 
The colours of the 310 solutions were brownish yellow. 

The 5 barium permanganate solution showed the bands well 
marked, and very little increase in the general absorption from 
the earlier observations — the bands 1, 2 and 3 were very faint 
and narrow in the 310 solutions, and just beyond this towards the 
ultra violet there was complete general absorption. 

In the 310 potassium permanganate solution the bands 1, 
2 and 3 were faint but they were better marked, and bands 4 
and 5 were only just visible, but they were wider, than the 
corresponding bands in the 5 solution. Just beyond band 5 on 
the more refrangible side there was complete general absorption 
in the 310 solutions. 

So that these experiments .prove that the changes of the 
solutions made in the dark and kept from the influence of light 
were very similar to those which had been subjected to the action 
of light ; although light appeared to accelerate the rapidity of the 

and the absorption spectra of various permanganates. 253 

. III. 

In order to test the accelerative effect of light, solutions of 
permanganate of zinc were made ; one series in the light, and 
allowed to stand in the full glare of the light of the laboratory, 
and another series of solutions made in the dark and allowed to 
stand well covered up with black cloth and placed in a cupboard 
to which no light could penetrate. The solutions standing in the 
light were examined by the eye from time to time. After six 
hours a very slight change in the usual permanganate tint of the 
310 solution was noticeable ; but none in the 154 solution. 
After 10 hours standing the 154 solution was still pink and the 
310 solution was rose coloured. On standing 24 hours, the 
310 solution was light yellow brown in colour, and the 154 
solution was rose red. The solutions appeared to retain this 
colour during another 24 hours. 

After two days standing, the solutions which had been made 
in the dark, and which had stood in the dark during this period 
of time, were then examined and compared with those kept in the 
light, and there appeared to be exactly the same changes in colour 
in them. 

L. Zinc perraanaranate in dark } ^ ^a i i.- 

1 ^ J® • r 1 J. r 154 solutions, 

do. do. m hght J 

do. do. in dark 5 solution. 

Band 1 was not quite so wide in the 154 dark and light 
solutions as in the 5 solution ; band 2 was also narrower in the 
154 solutions; band 3 was also narrower but not so well marked ; 
whilst bands 4 and 5 appeared to be slightly wider in the 154 
dark and light solutions. The general absorption in the solutions 
kept in the dark and in the light was about the same in each, 
and greater than that of the 5 solution. Also there was a 
slight shift of the bands in the 5 solution towards the red 
end more than in the 154 solutions, but the difference was not 
well marked. 

M. Zinc permanganate in dark 1 o-irv i j.- 
do. do. in light J 

do. do. in dark 5 solution. 

Band 1 was again not so wide in the dark and light 310 
solutions as the corresponding one of the 5 solution ; bands 
2 and 3 were also much narrower in the dark and light solutions ; 
whilst bands 4 and 5 appeared to be slightly wider in the dark and 
light 810 solutions than in the dark 5 solution. 

The general absorption of light in the solution kept in the 
light was a shade more marked than that kept in the dark ; 

254 il/?' Purvis, The influence of dilution on the colour 

and both general absorptions were greater here than those in the 
154 solutions. 

The shift towards the red end of the bands of the 5 solutions 
was much better marked when compared with those of the 
310 solutions than those of the 154 solutions. 

The solutions were allowed to stand as before in the dark and 
the light for two days longer and they were again examined. 

N. Zinc permanganate in dark 1 -, ^ . i , • 

1 ^ 1° • ,. 1, h 154 solutions, 

do. do. m light J 

do. do. in dark 5 solution. 

There was a very doubtful increase in the general absorption 
of the 154 solutions as compared with the previous observations in 
L, otherwise the differences in the appearances of the bands were 
very like those in the previous observations. There was no 
difference in the width and appearances of the bands of the 
solutions kept either in the light or dark ; the bands 2 and 3 were 
narrower in these solutions than in the 5 solution, whilst the 
bands 4 and 5 were very slightly wider. 

0. Zinc permanganate in dark 1 qi rj i f 
do. do. in light J 

do. do. in dark 5 solution. 

There appeared to be but a very slight increase in the general 
absorption of the 310 solutions as compared with the previous 
observations ; the bands 1, 2 and 3 were narrower than the 
corresponding bands in the 5 solution, the band 2 being the most 
marked in this respect, whilst bands 4 and 5 were slightly wider 
than the corresponding bands in the 5 solution. 

The shift of the bands towards the red end in the 5 solution 
was distinct as compared with their positions in the 310 solutions. 

The observations indicate that similar changes take place in the 
zinc permanganate solutions as in those of barium and potassium; 
and that light accelerates the changes. 

General conclusions. 

The results prove that, during the time of the observations, 
(1) in the stronger 5 solutions there did not appear to be any 
marked change in the ordinary colour nor in the absorption bands 
of the permanganates; (2) in the 154 solutions there were con- 
siderable changes in the colour which slowly turned to a rose red 
or reddish brown one accompanied by changes in the width of the 
absorption bands 1, 2, 3, 4 and 5 and an increase in the general 
absorption; (3) in the 310 solutions the changes in the colour 
were more marked and a brownish yellow colour was developed 

and the absorption spectra of various permanganates. 255 

with an almost complete obliteration of the absorption bands and 
a greatly increased general absorption ; (4) a shift of the bands 
of the 5 solutions to the red end of the spectrum as compared 
with their positions in the 154 and -310 solutions, and this 
shift appeared to decrease with increased refrangibility of the 
absorbed rays. 

In order to explain the different positions of the bands of the 
different solutions, the observations of H,, Becquerel* show that 
such differences depend upon the concentration — the greater the 
concentration, the greater the shift of the bands towards the red 
end of the spectrum. 

With regard to the other changes, attention is again called to 
the observations that the changes take place whether the solutions 
are subjected to the action of light or whether they are kept io the 
dark, although light accelerates the changes. One explanation 
is that the dissolved gases, the atmospheric gases, particularly 
carbon dioxide, may have been the influencing causes. Against 
this view is the fact that carbon dioxide usually converts man- 
ganates to permanganates very rapidly; and oxygen would scarcely 
act as a reducing influence, whilst nitrogen is completely inert. 
Nor could the changes have been caused by any dissolved organic 
substances, for the solutions were made in distilled water, and 
from pure crystallised salts ; and also, all the glass vessels were 
well washed before use with a warm mixture of hydrochloric and 
nitric acids. Nor could any organic substances have entered the 
solutions, for the latter were always kept well covered up. Never- 
theless, in order to eliminate the action of any extraneous gases or 
dirt, another series of solutions of potassium permanganate was 
made, and the glass bottles were filled to overflowing. The contents 
were isolated from the air by well ground stoppers. The bottles 
of one series were filled in the dark, and they stood in cupboards 
to which no light could penetrate. A similar series of bottles 
stood in a well lighted room and they were exposed to the full 
action of light. The changes in the colour of the solutions were 
exactly the same as in the earlier observations ; but those of the 
solutions exposed to the action of light were much quicker. Besides 
the colour changes, a small bubble of gas collected in the bottles. 
The absorption spectra were not observed. 

The explanation which seems to account for the changes 
is that the dissociating force of the water slowly acted upon the 

dissolved permanganates, so that the ionic condition of K, and 

Mn04, where R represents the metallic ion, broke down. One 

may imagine that the Mn04 ioii undergoes further dissociation 

* Gompt. Rend. Vol. cii. p. 106. 

256 Mr Purvis, The influence of dilution on the colour, etc. 

into MnOs and O, or into MnOa and O2. In such dilute solutions 
the tension between the molecules of water surrounding the ions 
must have been very considerable, and it may have been so great 
as to destroy the MnOj condition, so that further changes took 
place which became visible in changes of colour, in changes in the 
width of the bands and in the liberation of oxygen ; and these 
changes would be accelerated by the vibrations of light. The 
intermediate stages of the changes might be represented by the 
narrowing of the bands 1, 2 and 3 and the widening of the 
bands 4 and 5, and these might correspond to changes of the 
MnOj ions into MnOg and ions. The complete change in colour 
from the well known permanganate tint to a light brownish yellow 
colour in the more diluted solutions, the disappearance of the 
absorption bands, and the increased general absorption represented 
the complete change into MnOg and Oo. The MnOg would be 
dissolved in the colloidal condition, and it would be represented by 
the complete disappearance of the bands, and the increased general 
absorption, whilst the oxygen partly escaped. 


It has not been possible to reproduce all the original photographs comparable 
with them in clearness and precision. The reproductions on the plate are from 
photographs of original negatives enlarged one and a half times. The shaded parts 
represent light issuing through the solutions ; the light bands represent the absorp- 
tion bands ; and the lighter parts in the more refrangible regions represent general 

1. Barium permanganate, 154 solution. 

2. do. do. 5 solution. 

These solutions were made in the dark, and they were kept out of contact with 
the light during the experiments. They correspond to paragraph G in the notes. 

3. Barium permanganate, 154 solution. 

4. do. do. 5 solution. 

These solutions remained fully exposed to the action of sunlight. They corre- 
spond to paragraph B in the notes. 

It will be noticed that the weak band at \570 is almost obliterated, although it 
can be easily seen in the original photographs and in the enlargements therefrom. 
The narrowing of the bands at XX 546, 524 and the widening of those at XX 504, 486 
in the diluted solutions when compared with those in the stronger solutions are 
weU marked. 

5. Zinc permanganate, 5 solution made in the dark and kept in the dark. 

6. do. do. 154 do. do. do. 

7. do. do. 154 do. fully exposed to the action of light. 
These solutions correspond to paragraph L in the notes. 

8. Zinc permanganate, 5 solution made in the dark and kept in the dark. 

9. do. do. 310 do. do. do. 

10. do. do. 310 do. fully exposed to the action of light. 

These solutions correspond to paragraph M in the notes. 

The band at X 570 is only just visible; but the narrowing of the bands at 
XX 546, 524 and the widening of those at XX 504, 486 when compared with those in 
the stronger solutions are easily distinguishable. The general absorptions of the 
solutions 6 and 7 do not show very marked differences : but there is a little 
difference in those of the solutions 9 and 10. 

Phil. 8oc. Proc. xv., Pt iii. 

Plate XL 

o O '^ "=t ^ 
fS. -vt- Ol O 00 
to lO ^ 'O KJ- 

o ^ 


■^ o 

K -t 


O 00 

^n vD 


LO ^ 


Dr Barkla, Phenomena of X-Ray Transmission. 257 

Phenomena of X-Ray Transmission. (Preliminary Paper.) By 
Charles G. Barkla, M.A., D.Sc. (Communicated by Professor 
Sir J. J. Thomson.)* 

[Read 17 May 1909.] 

The principal phenomena accompanying the transmission of 
X-rays through matter may be classified under three heads — 
Absorption, Ionization, and Secondary Radiation. 

Much that has been written on these subjects has been in the 
form of disconnected papers, in which little attempt has been made 
to collect and classify known experimental facts, or to give an 
explanation of observed phenomena in terms of laws previously 
discovered. As a consequence X-ray phenomena have been made 
to appear much more complicated than they actually are. 

In the following paper it is intended to give, as briefly as 
possible and without entering into experimental details, a state- 
ment of facts already published, an account of the results of 
further experiments, and a survey of the whole subject of X-ray 
transmission, showing the connection between the various phe- 
nomena and accounting for apparent anomalies. As the phenomena 
of secondary radiation form the basis of classification they will be 
discussed first. 

Secondary X-Radiation. 

Secondary X-rays of two distinct types have been found to be 
emitted by substances subject to X-rays. Of these the scattered 
X-radiation — one of the same penetrating power as the primary — 
has invariably been found to be emitted during the transmission 
of a primary beam through matter. 

All the experiments that have been made on this radiation 
have strikingly verified the theory of scattering, as given by 
Sir J. J, Thomson -j-, many of the results being foretold as an 
immediate consequence of this theory. 

The second type of secondary X-radiation emitted by many 
elements, and probably by all, is a homogeneous radiation 
characteristic simply of the element emitting it. Unlike the 
scattered radiation this is distributed uniformly in all directions, 
and gives no evidence of polarization in a primary beam where 
such polarization exists. This radiation was shown by Barkla and 

* The expenses of these researches were partially covered by a Government 
Grant through the Royal Society. 

t Conduction of Electricity throuyh Gases. 

258 Dr BarUa, Plwiiomcna of X-Raij Transmission. 

Sadler* to be emitted only when the exciting primary radiation 
was of more penetrating type. Also it W7i,s shown that beyond a 
certain penetrating power of the primary, the intensity of this 
secondary radiation from a given mass of snbstance was pro- 
portional to the ionization produced by this primary beam in 
a thin film of air. As we have no exact method of comparing the 
intensities of beams differing in penetrating power, we are unable 
to determine accurately the relative amounts of energy of different 
beams reappearing as secondary radiation of this type. If, however, 
w^e assume as approximately true that the ionizations produced in 
a thin him of air by beams of equal intensity are proportional to 
the absorptions of these beams in air, we may also say that the in- 
tensity of this secondar}' radiation, beyond a certain penetrating 
power of the primary radiation, is proportional to the coefficient 
of absorption of the primary radiation in aluminium. The relation 
between the intensity of secondary homogeneous radiation and the 
absorbability of the primary radiation may thus be approximately 
represented by curve II in tig. 4. Whatever the accuracy of the 
assumption, the geueral features of the curve remain unquestion- 
able, i.e. lirst, no appreciable intensity until the primary is more 
penetrating; secondly, a rapid rise of intensity as the primary 
is made more penetrating ; and thirdly, a decline of intensity, ap- 
proximately, if not accurately proportional to the absorbability 
of the primary radiation. Mr Sadler f has recently investigated 
the curves in detail on the same assumption, using a series of 
homogeneous beams as primary radiations, and has found the 
same type of relation in all cases investigated. 

The secondary radiation from a large number of elements has 
been studied, and the percentage absorption of the radiation by a 
sheet of aluminium -01 cm. thick, as measured by the diminution 
of ionization in an electroscope 7 or 8 cms. from the radiating 
elements, has been published by the wTiter|. 

When subject to a beam of X-rays of only moderate penetrating- 
power, the radiation reaching the electroscope from elements of 
atomic weight between those of hydrogen and sulphur was almost 
entirely a sc^ittered radiation, none of the homogeneous type 
appearing. Later analysis of the radiations from other elements 
by Barkla and Sadler showed that the radiations fi-om the elements 
from Cr to Ag were practically homogeneous radiations, producing 
in general, ionizations several hvindred times the ionization pro- 
duced by the scattered radiation from the equal masses of the 
light elements. A weak scattered radiation was mixed with these. 

* '' Homogeneous Secondary Eontgen Eadiations," Phil. Mag., Oct. 190S, 
pp. 550 — 5S4. 

t •' Transformations of Eontgen Eays," Phil. Soc. Loud., April 23, 1909. 
ij; " Secondary Eontgen Eadiations,"' Phil. 2Iag., June 1900. 

Dr Barkla, Phenomena of X-Ray Transmission. 259 

The writer has recently investigated more closely the radia- 
tions from Sn, Sb, I (which have been recorded as elements 
emitting a radiation of variable penetrating power). It has been 
found that these consist of a very easy absorbed radiation and a 
very penetrating homogeneous radiation superposed. The absorp- 
tions of the penetrating portions of the beams from each element 
are shown in fig. 1 on curve B. The percentage absorptions of the 
soft radiations from these elements have not yet been determined, 
but they are roughly indicated on curve A in fig. 1. Though a 
full analysis of the radiations from W, Pt, Au, Pb, Bi, etc., has 
not yet been made, there is strong evidence that the observed 
radiations from these elements are also principally homogeneous 
radiations characteristic of the elements emittinsr them. 




--- >^n ,, 

<j ■ 

































Atomic Weight of Radiator 

Fig. 1. 

Note : Continuous lines connect points which have been accurately 


— Discontinuous lines pass through approximate positions of points, 

Dotted lines are hypothetical. 

A knowledge of these characteristic radiations is sufficient to 
account for the variations in the intensity and in the character of 
the secondary rays emitted by different substances, and for what 
have been regarded as anomalies in secondary radiation phenomena 
by a number of investigators. Thus the intense radiation from 
ethyl bromide when subject to a beam of ordinary penetrating 
power is that given by the element bromine — an element in the 
group of substances which emit homogeneous rays in considerable 
intensity when subject to an ordinary primary radiation. The 
variable behaviour of tin bichloride and of methyl iodide may also 
be explained in terms of the results for tin and iodine already- 
published. The variations are due to the fact that a beam of 
X-rays of ordinary penetrating power contains only a small 

260 Br BarJcla, Phenomena of X-Ray Transmission. 

proportion of rays of penetrating power higher than that of the 
penetrating rays from Sn, Sb, and I ; so that only a small pro- 
portion of the more penetrating radiation is emitted with the 
softer characteristic radiation. As the heterogeneous primary 
radiation is made more penetrating a greater proportion of the 
beam excites the penetrating secondary radiation. Thus the 
intensity of secondary radiation and the average penetrating 
power of this radiation increase rapidly. 

By an examination of the curves connecting the absorption of 
the various characteristic radiations with the atomic weight of the 
radiating substance as shown in fig. 1 we are led to several 
important conclusions. These characteristic secondary radiations 
may be divided into several groups, the radiation belonging to 
each group becoming more penetrating with an increase in the 
atomic weight of the radiating substance. Thus in fig. 1 we show 
groups A and B. 

If elements of low atomic weight emit characteristic secondary 
radiations belonging to groups A and B, these radiations must be 
exceedingly soft, and as a consequence must emerge from only a 
very thin surface layer of the radiating substance. Owing to this 
fact and to the absorption of the radiation in air before reaching the 
electroscope, the effects of these radiations must be very small. 
Such a soft radiation has been found to be emitted by Ca mixed 
with the scattered radiation, and there have been indications of 
such radiations from S and from Al. These, however, have not yet 
been examined carefully. 

As the atomic weight of the element increases, the character- 
istic radiations become more penetrating and produce much 
bigger ionizations in the detecting electroscope, almost completely 
swamping the effect of the scattered radiation. As the atomic 
weight of the element becomes higher still, the characteristic 
radiation becomes so penetrating that only the most penetrating 
constituent in an ordinary primary beam is able to excite it. The 
intensity of the secondary thus diminishes, and finally the radiation 
becomes inappreciable. But before this has happened the radia- 
tion belonging to another group has appeared in appreciable 
intensity, and this ultimately becomes the most important 
secondary radiation. It appears very probable that there are other 
groups similar to these, for even when the primary I'adiation is too 
" soft " to excite the radiations A and B it is absorbed and it 
produces ionization. And these secondary radiation phenomena, 
as we shall see later, are connected with the phenomena of ab- 
sorption and ionization. The hypothetical groups of radiations 
softer than those in group A we shall denote by the letter X. 

Dr Barhla, Phenomena of X-Ray Transmission. 261 


Experiments on absorption of X-rays have been made by a 
number of experimenters, but owing to lack of knowledge of 
secondary X-rays, and to heterogeneity in the beams experimented 
upon, little regularity of behaviour could be observed from the 
experimental results. 








^ 600 

■ ; 














^' 560 
.^ 48C 
















^ 360 




















/ ; 

1 240 






\ ^ 

/ ; 




'^ 160 





















i ///. 


\ \ 








-fi — 















IC 1 

50 14 

/lasoRPTlON /r/ /ll (Jl\ 
Fig. 2. 

The connection between the absorption of X-rays and the 
secondary radiation emitted from the absorbing substance was 
first shown by Barkla and Sadler in a paper on " Homogeneous 
Secondary Rontgen Radiations." The laws governing the absorption 
of X-rays have recently been more fully investigated*. The 

* " The Absorption of Bontgen Bays," Fhil. Mag., May 1909. 

262 Dr Barkla, Phenomena of X-Ray Transmission. 

principal features brought to light by the investigation are 
exhibited in curve IV in fig. 4, in which the absorptions by a 
given element are plotted as ordinates, and the absorptions by Al 
as abscissae. 

In all the absorbing substances examined — C, Mg, Fe, Cu, Zn, 
Ag, Sn, Pt, Au — there is approximate proportionality between the 
coefficients of absorption in a substance E, say and in Al through 
a wide range of penetrating power. This approximate pro- 
portionality holds until the primary radiation is made more 
penetrating than the homogeneous radiation characteristic of 
the absorbing substance R. Then the absorption begins to 
increase more and more rapidly until, after reaching a maximum, 
it begins to approximate again to proportionality with the absorp- 
tion in Al, the ratio of absorption coefficients being now much 
higher than before. The increase in the absorption was thus 
shown to commence at the same point as that at which the 
secondary homogeneous radiation began to be emitted, the con- 
nection between absorption and intensity of secondary radiation 
being shown by the curves IV" and II. As the range of penetrating 
powers experimented upon was that from the radiation characteristic 

of Cr f- in Al = 136 j to that characteristic of Ag (- in Al = 2-5 j, 

it will be seen by comparison with fig. 2* that all elements, 
one of whose characteristic radiations is between these limits, 
showed the same feature in the absorption curve. All those 
which did not emit a characteristic radiation of penetrating power 
between these limits gave absorption curves without any special 
deviation from the approximate proportionality. It is important, 
however, to notice several features of the curves. The shape of 
the curve for primary radiations is considerably more penetrating 
than that necessary to produce the characteristic secondary radia- 
tion in any substance approximated to the shape just previous to 
the sudden rise in the absorption, showing the possibility of a 
similar rise in the absorption having occurred with a much softer 

Again — and this is a most important point — the mass absorption 
coefficients for a given radiation are in the order of atomic weight 
of the absorbing substance when the corresponding radiations are 

Thus using the very soft radiation from Cr, - in C, Mg and Al 

are in order of atomic weight, but there is a step back for the 
elements Fe, Ni, Cu, Zn, Ag, Sn because in these the radiation of 
group B is not excited, and there is a further step back for Pt and 

* Reproduced from paper on " The Absorption of Eontgen Rays," Barkla and 

Dr Barkla, Phenomena of X-Ray Transmission. 263 

Au because in these the radiation A is not excited. When, 
however, the primary radiation is sufficiently penetrating to 
excite the radiation B in Fe, Ni, Cn, Zn, these take their proper 
place. A radiation sufficiently penetrating to excite radiation 
B in Ag, Sn, Pt, Au was not used, but when the radiation was 










_ Au 

'^/V''*' l/erT/ 'soft' Radiation 




^ -^ Rather 'soft Radiation 

^^y^,^^^^^ Fairly penetrating Radiation 

50 100 150 200 

Atomic Weight of Absorbing Substance 

Fig. 3. 
Note : Letters X , A and B denote the characteristic secondary radiations 
excited (see fig. 1). 

sufficiently penetrating to excite the radiation A in Pt and Au, 
these took their proper places with respect to Ag and Sn. 

Thus in fig. 3, curves I, II and III exhibit the relation 
between the absorption in different elements and the atomic 
weight of the absorbing element for three different radiations. 
Curve I was obtained by using the very soft homogeneous radiation 

VOL. XV. PT. III. 18 

2(34 Dr Barkla, Phenomena of X-Ra>/ Transmission. 

from Cr I - in Al = 13G 1 ; Curve II by the fixiily soft homogeneous 
radiation from As [ -in Al = 2:2'o j ; Curve III by the fairly pene- 
trating radiation from Ag ( - in Al = 2*5 1 . 

We thus see from these results that the absorption of a 
homogeneous radiation by elements of various atomic weights is a 
periodic function, but iu general an inereasiug fuuction of the 
atomic weight. Though observations have not been uiade on a 
suthcieut number of elements to obtain the accurate relation 
between absorption and atomic weight of the absorbing substance 
for any one particular homogeneous beam, ditierent portions of 
similar curves have been obtained from observation of the absorp- 
tion of other homogeneous beams, aud their shapes reproduced iu 
the discontinuous cur^'es iu the tigure. 


An examination of the results obtained by ditierent experi- 
menters on the ionizations produced in gases by X-rays showed 
that these phenomena were in all probability also connected with 
secondary X-ray phenomena, and that the numerous apparent 
irrecrularities mio-ht be explained in terms of laws similar to those 
found for absorption. The writer was therefore led to attempt an 
investigation of the ionizations produced in different gases by 
homogeneous beams varying considerably in penetrating power. 
The radiations used were the homogeneous radiations from Fe, Cu, 
Zu, Br, Sr, Ag, Sn, Sb, varying in absorbability as shown by curve 
B in tig. 1. * ^ 

The oases and vapours experimented upon were Air, 0, CO.3, 
SO,, CABv, SnCl,, CH3I. 

The results of preliminary experimeuts may be briefly stated 
as follows : 

Eange of penetrating power 
Gas of radiation Eesidts 

O Fe radiation to Ag radiation louization approximately proportional to 

ionization iu air 
COa ,, ,, „ „ ,, ,, „ 

CoHjBr Fe radiation to Br radiation ,, ,, ,, ,, 

Br radiation to Sn radiation Eelative ionization increased approximately 

SnCL Fe radiation to Sn radiation Ionization approximately proportional to 

ionization iu air 
I radiation ... ... ... Eelative ionization considerably greater 

CH3I Fe radiation to Ag radiation louization approximately proportional to 

ionization in air [only slight gradual 
change, if any] 

/)r Bar Ida, Fhenomena of X-Ray Transmission. 265 

These results must be connected with the results of experi- 
ments on secondary radiation and absorption. Carbon, Nitrogen, 
Oxygen and Sulphur, elements in the group in which an appreciable 
homogeneous radiation within this range of penetrating power 
has not been detected, and in which there is proportionality of 
absorption within this range of penetrating power, here exhibit 
proportionality of ionization also. 

Ethyl bromide and Tin bichloride exhibit a like proportionality 
in ionization until the radiation becomes more penetrating than 
the radiations characteristic of Br and Sn respectively. For more 
penetrating radiations the relative ionization increased just as the 
secondary radiation in Br and Sn began to be excited and as the 
absorption began to increase. 

/Ibiorpl.nii of .jic Radii 

biorption of Primary in Al. 

Fig. 4. 

Methyl Iodide, which was not subjected to a radiation of more 
penetrating type than that characteristic of Iodine, also exhibited 
approximately the same proportionality of ionization. 

We are thus led to the conclusion that as in the case of the 
secondary radiation and absorption, the turning point in the 
curves showing the relation between ionization and the pene- 
trating power of the primary radiation is just where the primary 
radiation becomes more penetrating than the homogeneous 
radiation characteristic of the substance traversed, or of one of the 
elementary constituents of the substance traversed. 


266 Br Barkia, Phenomena of X-Batj Transmission. 

General Discussion. 

The various phenomena may therefore be connected as shown 
in the diagram fig. -i. 

Line I represents the absorbability of the secondary radiation 
characteristic of an element R say. 

Curve II shows approximately the relation between intensity 
of secondary radiation from R, and absorbability of the primary 
radiation (measured in Al). 

Curve III shows the relation between ionization in R and 
absorbability of the primary radiation (measured in Al). 

Curve IV shows the relation between absorption in R and 
absoi'bability of the primary radiation (measured in Al). 

Curves II and III are based on the assumption that the 
ionization in air is proportional to the absorption in air for beams 
differing in penetrating power. The important features are beyond 
doubt ; the exact shape, however, depends on the accuracy of this 

There is thus an intimate connection between the absorption 
of a primary radiation in a substance, the ionization in the 
absorbing substance (when in the gaseous state), and the intensity 
of secondary radiation from the absorbing substance. These are 
periodic functions of the penetrating power of the primary radiation, 
the three rising and falling together. Though two complete 
periods have not yet been obtained in any one substance, there is 
very strong evidence from the behaviour of different substances 
that there are at least several maxima and minima to be obtained 
by using a primary radiation of sufficient rauge in penetrating 
power. The periodicity in intensity of secondary radiation is not 
one of intensity alone, tor each fresh period brings a characteristic 
radiation of different penetrating power. 

Sufficient experiments have not yet been made in order to 
determine if the periodicity is a true jjeriodicity in the behaviour 
of one system in the atom, or is due to different systems behaving 
in a similar manner wdieu subject to primary radiations of different 
penetrating powers. Be that as it may, the experiments on 
secondary radiation show that there are various characteristic 
radiations ; the experiments on ionization show that there are 
various ionizations, only a part of the total ionization being con- 
nected with one radiation ; the experiments on absorption show 
that there are various processes of absorption, only a part of the 
total absorption being connected with one radiation. 

It should perhaps be pointed out that it is owing to the fact 
that absorption, ionization and secondary radiation connected with 
one substance are periodic functions of the absorbability of the 
primary radiation, that these three quantities are also periodic 

Dr Barkla, Phenomena of X-Ray Transmission. 267 

functions of the atomic weight of the substance subjected to a 
fixed primary beam. 

Many experiments remain to be performed before any theory 
regarding the exact processes taking place during the transmission 
of X-rays through matter can be established. It is, however, 
worth while pointing out that if an electromagnetic pulse in which 
the electric force is uniform from front to back of the pulse passed 
over a number of independent electrons with a definite period of 
vibration, the absorption would be a periodic function of the thick- 
ness of the primary pulse. The absorption coeflficient might be 

irm d 

1 o ^ 

1 — cos ZTT k 

where d is the thickness of primary pulse and h the wave-length of 
the radiation emitted by the freely vibrating electrons, N the 
number of electrons in unit volume, e and m the charge and mass 
of an electron. This would give an absorption curve of somewhat 
the same form as those shown, and would also show periodicity. 
As we have no method of measuring the thickness of the pulse, 
and do not know anything of the force distribution in the pulse, we 
cannot strictly compare the experimental curve with this. 

It should also be pointed out that with a primary pulse 
in which the force gradually increases from zero to a maximum 
and gradually again to zero, the periodicity and indeed the 
absorption of thicker pulses would practically disappear. In such 
a case the periodicity would have to be explained by assuming 
the existence of different absorbing, radiating and ionizable systems 
in the same atom. 

The connection between absorption, ionization and intensity of 
secondary radiation might be easily accounted for. It would only 
be after such an absorption of energy that electrons would be 
hurled out of an atom, and ionization be produced — (both as a 
primary and secondary or subsequent effect of this ejection). The 
disturbance in the atom would set up an electromagnetic pulse 
characteristic of the atom. 

It seems very improbable for several reasons that the sub- 
sequent bombardment of other atoms by the ejected electrons 
produces an appreciable secondary X-radiation. The speed of 
ejection has been found to depend on the penetrating power of 
the primary radiation causing that ejection ; so also would the 
character of the secondary X-radiation produced by these. This is 
contrary to experimental fact. Again, the connection between 
the penetrating power of the primary radiation necessary to 
produce a certain secondary radiation and the penetrating 
power of that radiation would be very difficult to explain. 

^68 Dr Barkla, Phenomena of X-Ilai/ Tra^is^^mission. 

Lastly, preliminary experiments on the secondary radiation from 
alloys appears to indicate that the bombardment of a second 
substance by the ejected electrons produces no change in the 
character of the secondary radiation produced. The most difficult 
point to explain is the fact that the primary radiation must be 
just more penetrating than the homogeneous secondary radiation 
characteristic of the exposed substance for that radiation to be 
excited. This law appears to be an extension of Stokes' Law of 
Fluorescence to which the phenomenon of the secondary chai'acter- 
istic radiation is akin. 

The exactness with which the law is obeyed, and the striking 
similarity between the various absorption curves indicates a de- 
fiuiteness in the structure of the pulses, and the absence of 
anything corresponding to variation in pulse structure. 

As absorption of energy must precede the expulsion of electrons, 
we might expect to find the intensity of corpuscular radiation 
connected with the absorbability of the primary radiation in the 
same way as is the X-radiation, except that the velocity would 
vary A^ith the penetrating power of the primary beam, as has 
been found by Innes. 

A detailed account of these experiments and a fuller discussion 
will be published later. 


Mr Kaye, The Emission of Rontgen Rays, etc. 269 

The Emission of Rontgen Rays from Thin Metallic Sheets. 
By G. W. C. Kaye, B.A., D.Sc.i Trinity College, Cambridge. 
(Communicated by Prof. Sir J. J. Thomson.) 

[^Received 4 August 1909.] 

Prof. Bragg and Dr Madsen* have, from the point of view 
of the neutral-pair theory of the Rontgen and 7 rays, made 
measurements of the secondary corpuscular radiation which goes 
forward and backward when 7 rays are incident on thin metal 
sheets. They find in most cases a large want of symmetry in the 
distribution of these secondary rays — there is more " emergence " 
than " incidence " radiation : especially is this so for metals of low 
atomic weight. For example, the ratio {R) of the emergence 
intensity to the incidence is, in the case of soft 7 rays, about 13 
for carbon, 7 for aluminium, 2 for the metals of the copper group, 
1"1 for tin and lead : with hard 7 rays these numbers become 
20, 7, 3 and 1 respectively. 

Madsen f obtained similar results in his investigation of the 
distribution of the secondary 7 radiation produced by 7 rays under 
analogous conditions. For zinc R (defined as before) is about 5, 
for lead 7. He showed also that the 7 rays in passing through 
matter are softened as well as scattered. The distribution of the 
scattered radiation depends on the quality of the exciting 7 rays 
and also upon the nature of the scattering medium. The qualities 
of the incidence and emergence radiations are not alwa37s identical. 

CoOKSEY {Nature, Ap. 2, 1908) worked in like manner with 
the corpuscular secondary radiations from Rontgen rays, and brought 
his results into parallelism with those for 7 rays; although the 
asymmetry was very much less pronounced, R varying from 1*1 
to 2 for different elements. 

It remained for Bragg and GLASSON+ to find a corresponding 
lack of symmetry in the distribution of the secondary X rays 
produced by the transmission of X rays through thin metal sheets. 
The ratio R ranges from about 3 for Al to 1'3 for Pt. 

Quite recently Madsen § has extended the enquiry to /3 rays 
and found very similar results. The greatest value of R is about 
9 for Al and 4"5 for gold. He found that as the thickness of the 
metal screen is increased, the total emergent scattered radiation 
increases rapidly to a maximum (at '01 3 cm. Al and "OOOS cm. Au) 
and afterwards decreases. 

With some of the foregoing results in mind the problem of 

* Bragg and Madsen, Phil. Mag. 16, 1908, p. 918. 

t Madsen, Ih. 17, 1909, p. 423. 

+ Bragg and Glasson, Ih. 17, 1909, p. 855. 

§ Madsen, TrauH. Hoy. Soc. S. Australia, April, 1909. 


Mr Kaye, The Emission of Rontgen Hays 

the distribution of the Rontgen rays produced by the impact of 
cathode rays on a thin metal target invited attack. The simplest 
experimental conditions would be realised by the use of as thin 
a metal anticathode as can be obtained, and by employing cathode 
rays of uniform velocity. This latter condition is being satisfied 
in experiments now in progress, but as the cathode rays in soft 
coil-driven Rontgen ray tubes are not very heterogeneous it seemed 
worth while to carry out preliminary experiments in which the 
condition of homogeneity of the cathode rays was waived. More- 
over it has to be remembered that the Rontgen rays emitted will 
be diluted to some extent with secondary Rontgen rays produced 
by the action of the primary X ray beam on the material of the 
anticathode. It remained to see what effect this would have on 
the distribution of the primary rays. 



The apparatus is sufficiently indicated by the figure. An 
anticathode of thin metal leaf was mounted centrally in the 
tube BJE, so that it could receive a pencil of cathode rays from 
either side at an angle not far removed from the normal. The 
X rays produced could pass out normally by the aluminium windows 
D and E which, needless to say, were equally thick ('Ol cm.). 
The idea in providing two cathodes G and C was to guard against 
any possible want of symmetry in the apparatus. Plane cathodes 
had to be employed ; such thin leaves as were used for anti- 
cathodes puncture at once if any attempt is made to focus the 
cathode rays. The tube was coil-driven. 

from Thin Metallic Sheets. 


The intensity of the X rays was measured by an ionisation 
chamber / (with thin aluminium bounding walls), and a Wilson 
electroscope : the usual insulation and shielding precautions were 
taken. If the rays were cut down by a screen, it was, of course, 
inserted between the aluminium window and the ionisation 

The anticathode was earthed and put in metallic contact with 
the tube-anode A or A'. The whole of the discharge tube could 
be slewed round by means of the mercury-trapped ground-joint J, 
which led also to the pump. Thus the X rays proceeding from 
either window could be measured by the one ionisation chamber : 
one had only to rely on the constancy of the discharge. 



Thickness of 

Spark Gap 

Thickness of 
Al. Screen 

^ Emergence Rad. 
Incidence Rad. 

•1 cm. 



•022 cm. 




•033 „ 

•044 „ 



•5 cm. 




•8 „ 



•5 cm. 

•047 cm. 


•00002 cm. 

1^5 cm. 




•022 cm. 



•047 „ 


•00003 cm. 

•5 cm. 



1-5 „ 



•1 cm. 






•022 cm. 


•00001 cm. 

•7 cm. 




r7 cm. 

•047 cm. 



•047 cm. 


•00002 cm. 

•7 cm. 



1-7 „ 




•000042 cm. 

•2 cm. 



272 Mr Kaye, The Emission of Rontgen Rays, etc. 

In these preliminary experiments, aluminium, copper, gold 
and platinum leaf were used for anticathodes. A few typical 
measurements of the ratio R of the intensity of the emergent to 
the incident radiation are appended. Platinum behaves like gold 
in the values that it yields for the ratio under different conditions. 
The speed of the cathode rays, being dependent on the potential 
between the cathode and anode, is sufficiently indicated by the 
length of the alternative spark gap (between large brass balls). 

These and other results indicate the following points: — 

1. Generally speaking the emergence Rontgen radiation from 
a thin metal anticathode exceeds the incidence in intensity. This 
is most marked in the case of aluminium. Furthermore, as evi- 
denced by the phosphorescence of the glass walls of the tube, the 
accompanying emergence secondai-y cathode radiation from the 
anticathode is more intense than the incidence cathode radiation. 
As far as could be judged " R " for the cathode rays seems to 
follow any variation of " R " for the X rays. Madsen's results 
(above) for /3 rays may be noted. 

2. With heterogeneous cathode rays the incidence beam of 
Rontgen rays is softer than the emergence. 

3. The ratio {R) of the emergence intensity to the incidence, 
increases with the speed of the impinging cathode rays, provided 
the anticathode is thick enough. This is shown both by increasing 
the potential on the tube, and by sifting out (with screens) the 
softer X rays produced by the more slowly moving constituents of 
the heterogeneous bundle of cathode rays. 

4. For each thickness of anticathode there is a certain speed 
of cathode ray which gives a maximum value to the ratio R. The 
ratio drops in amount for greater or less speeds than this. 

5. As the thickness of anticathode increases, the emergence 
intensity (for the same speed of cathode ray) first increases to a 
maximum and then dies away ; the incidence intensity meanwhile 
gradually increases to a constant value. The resemblance to 
Madsen's results for ^ rays (above) will again be noticed. 

A discussion of the results is reserved until the measurements 
are concluded. 

I wish to thank Sir J. J. Thomson for his interest in these 

Mr Crowther, On the Scattering of jB-rays, etc. 


On the Scattering of the ^-rays from Radium hy Air. (Pre- 
liminary Note.) By J. A. Crowther, M.A., St John's College. 

[Received 18 August 1909.] 

In a previous paper* I have described some experiments on 
the scattering of a beam of the ;8-rays from Uranium by thin 
sheets of various solid substances. It was shewn that a very 
thin sheet of metal was sufficient to produce almost complete 
scattering in a narrow pencil of /3-rays ; and further that the 
diminution in intensity of a definite pencil of rays due to 
the scattering of the rays, might be expressed by an exponential 

The present paper contains a brief preliminary account of 
some experiments, still in progress, on the scattering of a beam 
of /3-rays from Radium during its passage through Air. 

A pencil of y8-rays from Radium is spread out into a magnetic 
spectrum, a portion of which, consisting of rays having a definite 
small range of velocities, falls on a small aperture in a lead 
screen. The rays passing through this aperture are further 
limited by a second screen, so as to form a narrow divergent 
pencil of small angle consisting of rays of very nearly the 
same velocity. The intensity of the /3-radiation passing through 
the geometrical cross-section of this pencil, at various distances 
from the origin, is measured by the ionization produced in an 
ionization chamber. It has been found that if /„ is the initial 
intensity of the pencil of /3-rays, and I the intensity passing 
through the geometrical cross-section of the beam at a distance d 
from the origin, then 

where cr is a constant, which may be called the coefficient of 

The following table gives the values of a for ordinary air 

Velocity (cm. /sec.) 

a (cm.-i) 

V .^Jff 


2-26 X IQi" 


rei X lo^" 

r98 X 10i» 













* Proc. Roy. Soc. A, Vol. 80, p. 186. 1908. 

274 Mr Croii'ther, On the Scattering of ^-rays, etc. 

for various velocities of the jB-r^yQ. The first cohimn of the 
table gives the velocity of the rays employed, as calculated from 
their magnetic deflection ; the second column the corresponding 
value of a, the coeflicient of scattering for air at normal temperature 
and pressure. The third column gives the value of the product 
V \la, where v is the velocity of the rays employed. It will be 
seen that the coefficient of scattering of the rays varies rather 
more rapidly than the inverse fourth power of their velocity. 
This is probably due to the increase in the electrical mass of the 
/S-corpuscles with increasing velocity. Prof. Sir J. J. Thomson * 
has shewn that the coefficient of scattering is roughly propor- 
tional to li'v^m-, where v is the velocity and m the mass of the 
/S-corpuscle. Assuming the Lorentz formula for the change in 
mass of an electron with change of velocity, we have 

where /3 is the ratio of the velocity of the corpuscle to the velocity 
of light. Taking into account, therefore, this change of mass with 
velocity we should have 

(1 — /3-) "*.■?;. Xja = constant. 

The last column of the table, which gives the values of this 
quantity, shews how far this is the case. 

* See Conduction of Electricity through Gases, p. 377. 1906. 

Mr Vegard, On some general Properties, etc. 275 

On some general Properties of Mixed Solutions. By L. Vegard, 

Universitets-stipendiat of Christiania University. 

[Received 9 June 1909.] 


§ 1. The object of the following paper Avill chiefly be to 
generalise some results concerning properties of solutions, which I 
have given in a previous paper*. The results found in this paper 
were, in short, the following : 

I. Determination of the variation of concentration in a binary 
solution exposed to any field of gravity. 

(a) Applying a purely mechanical equilibrium condition, it 
was proved that the concentration in the equilibrium state must 
be constant along an equipotential surface and have its greatest 
slope in the direction of the force. 

(6) The concentration gradient Avas found from the condition 
that a small volume element acted on by gravity shall be in 
thermodynamic equilibrium. The result found holds good for 
any concentration and without regard to the volatility of the 

(c) In the case in which the osmotic pressure is known as a 
function of concentration, the concentration gradient can be found. 
Numerical calculations were carried out for cane sugar under the 
assumption that the osmotic pressure follows the gas laws. In the 
case of electrolytes, the equation had to be slightly modified, and 
the calculation was carried out for potassium hydrate. 

II. (a) Using the conception of osmotic pressure, some very 
interesting relations were found connecting the concentration 
gradient with the variation of osmotic pressure with hydrostatic 
pressure. These relations Avere : 

,^ , 1 (d'7r\ dc dir 

(1) P-Po=K[Tcl,d^>^Pdp' 

,^. 1 /d'7r\ dc dir 

(2) p-p„= XT + Po^ ' 

K\dc Jp^ dn ^ dpa 

(3) ^J^{l+^J^ 
dpo dp\ dpo 

p is the density of the solution at pressure p; Pq that of the 
solvent at p^; ir = p — po — osraoiic pressure, p and jy^ being the 

* "Beitrage zur Theorie der Losungen." Christiania Vid. Selsk. Skr. No. 8, 
1906. Phil. Mag. [6] 13, p. 589, 1907. 

276 Mr Vegard, On some general Properties 

pressure on the solution and solvent respectively. The relations 
(1, 2, 3) are quite general for binary solutions. They hold for any 
concentration without regard to volatility of the compounds, and 
the fluids may be compressible. 

(6) As a corollary from the three equations it was found that 

in sfeneral ( ^r- 1 !^wd 1 ^r- ) must be different, or the variation 
^ _ \dcjp \dcJp, 

of osmotic pressure with concentration will be different according 

as the pressure during the variation is kept constant on the 

solution or on the solvent. 

The problem we shall deal with in the following is to find the 
distribution in a solution containing an arbitrary number of sub- 
stances acted on by any field of gravity, provided equilibrium has 
set in and the tempeiature is constant all through the system. 

We shall treat the problem in two ways: in one we shall use 
the thermodynamic potentials, in the other we shall make use of 
the conception of osmotic pressure. But as the osmotic pressure 
up to the present has only been defined for binary solutions, it 
will be necessary to extend it to solutions in general. 

Part I. — Solution of the problem by means of 
thermodynamic potentials. 

1 2. Some properties of thermody mimic potential functions. — Let 
the solution be composed of {r + 1) substances 0, 1, 2 ... /•, with mo- 
lecular masses i)/o, i/j ... M,., and let the concentration be measured 
by the number of gram-molecules in unit volume ??„, "i, »2 ••• >h-, 
which in the case considered will vary from one point to another. 
In the followins; the concentrations as well as their first derivates 
will be considered as continuous functions of the coordinates. In 
the case of varying concentration, the thermodynamic potentials 
of the solution will no longer be homogeneous functions with 
respect to the total mass of each component ; but we must be able 
to assume, considering the thermodynamic potential Aco for a 
volume element Av, that when Av approaches zero Aco will 
approach the value it would have if the element had contained a 
homogeneous solution with concentrations equal to those at any 
point inside the element. Thus we can put 

Ao) = If {Anio, Anil , Am^ . . . Am,., p, T), 

where Am^,Am-^ ... Am,, are the masses inside the element and H 
is the same function as in the case of a homogeneous solution. T is 
the temperature, which is supposed constant, p the pressure on 
the element. Putting A»i, = il7,»(Ai' : 

Lim -r— = 0)' = H (MqUo, il/i?2i . . . M,.n,., p, T) ; 


of Mixed Solutions. 277 

ft)' is the thermodynamic potential per unit volume at the point 
considered. The thermodynamic potential for the whole system 

(4) o3=\\\ (jd'dxdydz. 

ft)' being a homogeneous function of the first degree*, 

(5) ft)' =f,M,n, -^f,M,n, + . .JrMrUr 

= (/>oWo + ^1 Hi + . . . ^r^r- 

/,,yi ...y";. are the thermodynamic potentials per unit mass of 
the various components. 

(j)fi,(j)i ... ^r are the thermodynamic potentials per gram- 
molecule of the various components, and 

(6) ilf,/,= <^,= |^; 

(f)i being homogeneous of degree with regard to no, iii ... riy, 


and since 

(7a) ^'^^\ = 0, 

5=0 07ls 

(75) d^^d^^ 

(7c) ¥^^.i, = 0. 

Let ft) be the thermodynamic potential for constant pressure. 

(8a) -^ = (volume) = 1, 

or by means of (5) 


(86) 2/AiWi = l, 

where fxi is the molecular volume of the component {i) under the 
conditions present. Let hn^, Sti^ ... Sfiy be simultaneous variations 
of 7?i, ^2 ... Ur. Then from (86) and (7a) 


(9a) XfiiSrii = 0. 

The expression to the left in equation (86) is a function of 
{xyz), and its total differential must be equal to zero, but as {xyz) 
are independent variables, the partial differentials with regard to 

* See Duhern, Mecanique Chimique, tome iii. livre vi. 

278 Mr Vegard, On some general Properties 

X, y and z must be equal to zero. Then differentiating equation 
(8b) Avith regard to x, and remembering that —^ = 0, 

(96) 2.,^' = 0. 

Taking the variation of the equation (96), 

X .S(^] + 'i'' ~* v"^ ^ 8n = • 
' \da;J ;=o dx ^=0 ^'>h " ' 

but the last term is equal to 

s=o ons j=o dx 



(9c) i^Jc,h{i^ = o. 

§3. Thermodynamic equilihrium conditions. 

As is well known, the condition for thermodynamic equili- 
brium at constant temperature can be expressed 

(Stk = (6^^)«„ 



■yjr is the internal thermodynamic potential =/ + >S^, where / is 
the iuternal energy, S the entropy. SA is the work done during 
the variation by the external forces acting on the system. The 
equations (10) express that for any independent variation the 
system may suffer the change in '\Jr must equal the work done. 

The equilibrium of our fluid system is not disturbed if we 
assume that a closed surface is laid inside the fluid and this 
surface becomes rigid. Moreover, the equilibrium is maintained 
if we imagine that an element of the surface is replaced by a 
movable piston pressing against the fluid with a pressure P equal 
to that existing in the fluid at the element considered. Thus we 
are quite free as regards choice of bounding surface. 

The field of gravity to which the system is exposed we shall 
assume depending on a potential U, where U, as well as its first 
derivates, are supposed to be continuous in the space occupied by 
the system. 

Now we get 

B{A)^- PS jll dxdydz - S ffL Udxdydz, 

of Mixed Solutions. 279 

and by means of (4) the equilibrium condition can be expressed 

8ff[(ir' + pU+P)dxdydz=0, 

or introducing the thermodynamic potential for constant pressure co' 

s(l{ (co' + pU+P-p) dxdydz = 0. 

The variation must be subject to the condition that no mass 
leaves the boundary. Putting 

(11) c'^-pU+P-p=W, 

we get the equilibrium conditions 

(12a) 8 \\\w dxdydz = 0, 

( 1 26) S Ului dxdydz = 0, i = 0, 1, 2 . . . r. 

(12c) 8 pdxdydz =0. 
(12c) is of course a consequence of (126). 

§ 4. Solution of the problem of variation. 

We shall now specify our bounding surface; and, as we have 
seen, this can be done without restricting the generality of the 
solution. We shall consider the fluid inside a parallelopipedic 
element {/^x. Ay, Az), and, for the sake of simplicity, one of the 
corners may be at the origin of the coordinates. Further, we shall 
let the element have a needle form, or we put 

Ay = aaAx'>^\ Az = a^Ax""^, 

where a^ and a.^ are finite quantities and Wj and n^ are positive 
numbers, which can be given any values we like, and thus we can 
always be able to put 

%i 5 2 and no ^ 2. 

The two ends of the element we shall denote by (0) and (1). The 
element is supposed to have rigid boundaries except at the end, 
which consists of the piston exerting a pressure P. 

We shall specify the variation, which consists in a relative 
displacement of masses inside the element, by supposing that 
the masses are suffer a translation parallel to the principal axis of 
the element. Under these conditions the equilibrium conditions 
take the form 

VOL, XV. PT. III. 19 


Mr Vegard, On some general Properties 

^ sf ^' Wd.v = = 1I\S (Ax) + I ^'S Wdx, 
Jo Jo 

g md^c = = ni'S{Aa') + I Siiida:, t - 0, 1, 2 ... r. 

Jo Jo 

fAX fAx 

S pd.r =0 = p,S{Aiv)+ Bpdx. 
, J Jo 


Wi, Ui, pi are the values of TF", ui and p at the end (1) of the 
element. We develop the functions W, ni and p after Maclaurin's 
formula, and, forming the variations, we get 

SF=STFo+s(^) .^• + etc., 

Sn; =8 nf + 8 i ~ ] x + etc., 
8p =8po+8(-~] w + etc. 

These values put into (13), and integrating 
(14a) F.^-^> + SFo4-iSf^) A.+ ...=0, 


dx Jo 

(146) n/^~^ + 8nf + ^8(p) Ax + ... =0, i = 0,l,2...r. 

(1.0) ,.«-^) + 8,. + p(gU.+ ... =0. 

To find 8 (Ax) we shall apply equation (146); we multiply 
with fi/ and add 

(i5„) ?^>i ,; ,,' + f ./(*..« + p (^■) A. ... ) = 0. 

fii' is the value of fXi at the eud (1), 

Putting the expression for fii into (15rt), and using the equa- 
tions (86), (9«) and (9c), 

Ax KdxJoX \dxjQ 

Using equation (146) 

(15.) ^>(l-A.i^-„,')=«A..+ ..., 


of Mixed Solutions. 281 

where a is a quantity containing some linear relation of the form 

a^h ,- -*, j9 ^ 2. We may at once remark that if the value for 

8 (Aa?) is put into (14) and we go to the limit A^ = 0, we find that 
the term depending on S (A^) disappears. 

From equation (11) we get 

Po being the pressure at the bounding surface is not altered by 
the variation. Putting these expressions into (14a) and using 
(14c) and (15) 

where etc. is of the form a^Ax'i + a^Aw'^^^ + ... q^ 2. 
From equation (5) 

\dxJo \dx/o \dxjQ o\dx/o 

Putting the expressions for Sooo and S ("j-") ^^^^ i^^)' ^^^ 
using (146) the equilibrium conditions take the form 

or letting Ax converge towards zero 

We drop the index (0), and remember that all values refer to 
the same point 

8p =iMs8n„ 

These values put into (17) give 

^ ^ s=o\ ' dx i=Q dus dx) 



Mr Vegard, On some general Pi'operties 

or putting for brevity's sake 

^ dx j=o dug dx 
and remembering equation (9a) 

\QMq + Qihn^ + ... Qr^nr = 0, 
[yLto S/Zo + jx^ hh + ... fi.,. Sn,. = 0. 

The equations (19) must be fulfilled for any variation Sni con- 
sistent with the two equations, then 


(20) ^' = ^=... = ^ = XQ,n, 

H'O M'l f^r 

Forming by means of the expression for Qg the sum to the right, 

^^ dU 

AQsns = p- 


The equations (20) and (9b) then give 

'd<f)o duo d(f)i d7ii dcf)). dn,. d U 

duo dx 9wo dx " dnQ dx dx 


{pfi,-M,) = = E„ 

dn-^ dx dui dx 


d^dno d^drh 
dn,- dx dn,. dx 


d(f),. dUr 

dn^. dx 


'^(pf.r-Mr) = = E,, 

/*o V7 + /ii-Tf +.../*. -^ = 0. 



We have here apparently (r + 2) equations between the (r + 1) 
unknown -j-^, ~, ... -j-^; but they are not all independent, in fact 

(ajiA/ ijjOG 


the following linear relation exists 

EoUa + j&\wi + . . . E,.nr = 0. 
The solution of equations (21) gives 

and for the other axis 




= A 


dx ' 





(22) dni = DidU. 

^ ^ T) 

dz ' dz ' 

of Mixed Solutions. 283 

Thus we see that also in the general case the concentration in the 
equilibrium state must be constant along a potential surface, and 
for the same concentration pressure and temperature the con- 
centration gradient will be proportional to the force intensity at 
the point considered. 

The equations (21) determining the concentration fall in any 
direction are perfectly symmetrical with regard to the (r + 1) 
components. The solution found holds regardless of compressi- 
bility of the solution and of the aggregate form of the single 
components, and for any concentration whatever, that may have 
physical existence. 

§ 5. Transformations. 

During the theoretical development we have assumed that the 
concentration is defined as the number of gram-molecules per unit 
volume. There are, however, several other ways of expressing the 
concentrations, and it may be useful to find the expression of our 
equation system corresponding to the most usual forms of concen- 

1. The concentration is defined as the mass of each component 
contained in unit volume. Let us call these concentrations 
Co, (7i ... Or, then 

Ci = Mini. * = 0, 1, 2...r. 

Introducing <^i = Mifi, 

and — = Qi, 

dfdC^dfdG, k.^-^(,a-l) i~0 12 r 

dCo dx '^dG, dx ^•■' dCr dx dx ^P^' ^' *-"'-^'^-"^- 

I cZC/q , dCi dUr ^ 

qi is the volume which unit mass of the component (i) occupies 
in solution under the conditions present. 

2. The concentration is given as the amount of mass of each 
component contained in unit mass of solution. Call these con- 
centrations ao,(Ti ... (Tr, then 

Ci Ci 
ai= ~ = . 

" 20. 

Employing well-known rules for transformation 

li^da^^^pd^^ JJ,d^M _ .^ 0, 1. 2 ... r. 

ocTo dx dcTi ax oar dx dx ' 

(23) -i 


d(Tn ttCi ttCTj. ^ 

— - + ■ — - + ... — - = 0. 
dx dx '" dx 


Mr Vegard, On some general Properties 

3. We choose one of the components, e.g., the first one as the 
principal component, and we express the concentrations of the 
others by the ratio between their masses and that of the principal 
component, all masses being united in the same volume element, 




We have 

Cj — ^ , C2 — ri ••• ^r - 


dGi _ dCo ^ dci 
dx ""' dx ° dx ' 

dfi dfidc, dfidc. 

dfi dCr 


dCo dCs dGs ' 

s = l,2 

Forming the expression in equation (23) and putting 

qip-l = ai, 
we get the following system 

(25) I'M^^^a,^. 
s=i dCs dx ^ dx ' 

i=0,l,2 ...r. 

In this case there are only r concentrations, and consequently 
r unknown. If we drop the first of the (r + 1) equations (25), we 
get the following solution 


9ci 9c2 " ' dci ' ' ' dcr 


dci dc^'" dci ' ' ' dCr 
8ci dCo'" dCi ' ' ' dC). 

'dfr dfv dfr 

9ci 9c2 " ' dCi 




9ci 9c2 ' " * 9ci_i ^ 9ci+i ' ' " dCr 

dCx dCo" 9C;_i " dCi+i ' ' ' dCr 

dci_ dCo'" dci-i ^ dCi+i ' ' ' dc,. 

dfr dfr 

dfr dfr 


C/ r 

dci 9c2 ' " 9ci_i dci+i ' ' ' dCr 


To find ^Nve must know the r quantities ai,a.2... oir, and, 

besides, a number of quantities derived from the thermodynamic 
potentials. As we have 

dCs dci ' 


of Mixed Solutions, 285 

the determinant to the left is symmetrical, and the number of 
thermodynamic quantities reduces to \r{r + l). For a binary 
solution we get the very simple result 

dfodcx _, .dU 

9ci dx dx 

In the earlier paper* the quantity q^, is found for binary solutions 



= ^o = ^,|p + c.(H-c,)3^}, 

dfa dc^ _1 ^ ^^ ^ ^^dp dU 

which is the same result as that found in the previous paper. 

and |:.-. = ic,(l+o,)|^^, 

dCi dx p oCi ax 

Part IL — Extension of the conception osmotic pressure 
to solutions in general. 

I 6. In the previous development we have seen that the 
thermodynamic potentials are very apt for a general mathematical 
treatment. The thermodynamic quantities appearing in the 
equations are mathematically very simple, all of them being 
derived from a single function by means of a simple mathematical 
operation. In spite of their mathematical simplicity, the thermo- 
dynamic potentials have their disadvantages when we are trying 
to get a clear idea of what they contain physically, and their 
interpretation is in fact the important thing when we are going to 
utilise them in any special case. Here it is that the importance 
of the osmotic pressure comes in ; and even if we consider the 
thei'modynamic potential to be the basis for the theory of solu- 
tions, the generalisation of the conception of osmotic pressure will 
still be of importance for a general treatment of solutions. The 
equations connecting the osmotic pressure with the thermo- 
dynamic potentials are from one point of view to be regarded as 
equations defining the osmotic pressure, but will at the same time 
give a physical interpretation to the thermodynamic functions. 

The conception of osmotic pressure may be generalised in a 
number of ways ; it will be our task to find the most usefid. Let 
the solution, as before, consist of {r + 1) substances, and suppose 
that we have a membrane permeable to {i) of them but imper- 
meable to the rest. The solution may be supposed to be con- 
tained in a cylinder and the membrane to have the form of a 
piston. We imagine that there is at first no fluid above the piston. 
If we apply a pressure sufficiently high, some substance of the (^) 

* Phil. Mag. [6] 13, p. 599. 

286 Mr' Vegard, On some general Properties 

components will pass through, forming above the membrane a 
solution, which we may call the secondary solution of the osmotic 
system. By diminishing the pressure, the current through the 
membrane will be less, until for a certain pressure an equilibrium 
will set in. There will be (i) equations determining the equili- 
brium state ; from these the (*' — 1) concentrations of the secondary 
solution, as well as the osmotic pressure, will be determined. 
When the osmotic pressures are derived in this way we shall say 
that they are formed upon a given solution. 

The number of osmotic systems that can be formed upon a 
solution is 

^^i\{r-i+l)\ ' 

For a binary solution iV = 2. 

For a solution containing three components. . . N =Q. 
For a solution containing four components ... iV= 14. 
For a solution containing five components ... iV^ = 30. 

The most important of these systems are those we get for ^ = 1 
and i = r. 

§ 7. The partial osmotic pressure. 

When the membrane is permeable to all but one component, 
we get an osmotic pressure which is analogous to the partial 
pressure in a mixture of gases ; we may call it the partial osmotic 
pressure for the component considered. 

Let the membrane be impermeable for the component (r), and 

let Ci' = — T, c/= — ^, ... Cr-i= — ^-r- be the concentrations at the 
nio vIq mo 

secondary solution. The equilibrium conditions are expressed by 

the equations 

(28) /,=//', i=0,l,2...(r-l). 

fi = Fi {Ci, Ci ... Cr, P) = thermodynamic potential per unit mass 

of component (i) in primary solution. 

fi'=Fi{ci,Ci...c'r-i,0,pr)\= thermodynamic potential per unit mass 

of component (i) in secondary solution. 

P the pressure on the primary, p,. that on the secondary solution. 
If Ci, Ca ... Cr, P are supposed to be given, the r equations (28) de- 
termine the r unknown Ci,C2 ... c'r-i,Pr- What interests us is 
the osmotic pressure Qr = {P —pr)- 

In order to get a nearly exact expression for this pressure we 
shall assume that in the state of equilibrium the differences 
Ci — Ci are small quantities; or, that the substances for which the 

of Mixed Solutions. 287 

membrane is permeable have nearly the same mutual proportion 
on both sides of the membrane. On this supposition, neglecting 
quantities of second order 

where // = F (ci , Ca . . . c,._i , 0, pr)- 

We multiply the equations (28) with 1, Ci, Ca ... c,._i in succes- 
sion and add them together, and inserting the value for ff 

r-X s=r—l i=r-l^f. 

(29) l>{fi-f/)Ci= X (c;-c,,)2 ^c, 

where we have to remember that Cq = 1. From equation (7a) we 

From a well-known property of thermodynamic potential 
-^ = qi where qi is the volume occupied by unit mass of the com- 
ponent (i) in a solution of the same substances as the secondary 
solution, but with concentrations equal to those of the primary one 
Ci, Ca ... Cr-i. Then 

Fi (ci, c.2... Cr-i, 0, P) -Fi{ci,Co... Cr-i , 0,pr) = I q/ dp. 

J Pr 

Fi (Ci, C,... Cr-i, Cr, P) -Fi{c^,C,... Cr-i, 0, P) = \'' p dCr- 

Jo OCr 

Adding these two equations together 

fi -fi = j ^ dcr +\ qldp. 
Inserting into (29) 

(^«> rci'a^"')''^"=-/i(tc'''--'"')*' 

but T |£'c; = _c,|i:, 

r- 1 ^ y 

■i qi Ci'= J r7> , 


where V is the volume of a solution with concentrations 
Ci , C2 . . . Cr-i and (77io)" the amount of mass of the component (0) 
contained in the same solution. 


288 Mr Vegard, On some general Properties 

Equation (30) then takes the form 

{mo)" mo 

• jr in 


Pr Jo 

Mr g/ 

mr TT^ dm... 

In general we have 

^= ,„.. \ ■ -0,1. 2... (.-1). 
V dp I 7n^ ;r^ dm^ 

Pr J omr 

Taking the sum of these equations from i = to i=r — 1, 

r—l r—1 

^(mi)" S mi 

I V'dp mrr^dnir 

Jpr h (^l^r 


but — = .^-, — r77 = specific volume of a solution of .concentrations 
p Z{mi) _ ^ 

Ci, Ca ... c,._i , and introducing 

mo + mi + ... mr-i 
the osmotic pressure will be defined by the equation 

(31a) [''-, dp = p/f, 1^ dKr. 

1 . 1 . . 

If — > is the mean value of - in the interval P — »,. we get for 

pm p 

the osmotic pressure Q,. 

(316) Qr = pjf^jKr^^dKr. 

This expression is well known for binary solutions, and we see 
that with a proper modification of the quantities p^, Kr and f^ 
the same expression holds for the partial osmotic pressure. 

§ 8. Osmotic pressure of the first order. 

When the secondary solution only contains one substance, we 
shall designate the corresponding osmotic pressure to be of the 
first order. Let tti denote the osmotic pressure, when the mem- 
brane is permeable to the substance (^). From the (condition of 
equilibrium we get in the usual way 

(32) -p= ^dp=gi-U 

Pmi J Pi Pi 

of Mixed Solutions. 289 

fi = thermodynamic potential per unit mass of component (t) of 
the solution at pressure Pi. 

gi = thermodynamic potential per unit mass of pure substance (i) 
at pressure P^. 

Pi is the density of the pure component (i), and pmi its mean value 
between Pi and pi . 
Partial derivation of (32) with respect to Cg gives 
, dFi{c„ c^...Cr,Pi) ^ _ J^ /BttA 

8Cs PmiydCs^p.' 

Assuming that the pressures on the solution Pi are the same 
for all osmotic systems and equal to p, the equation (33) will give 
an expression in terms of osmotic pressure for all the thermo- 
dynamic quantities appearing in equation (26). 

From the equation (27) we get the following relation 

(34) L (^A = 1. fijLA . 

Pmi \OCg/p Pms X^^i ■/ p 

This interesting reciprocal relation between the osmotic 
pressures of the first order, which is a simple corollary from their 
connections with the thermodynamic potential, would have been 
very difficult to obtain from a separate consideration of the 
osmotic pressures themselves. 

Part III. — The effect of gravity upon solutions found by 
means of the osmotic pressures of the first order. 

§ 9. The osmotic pressure of the first order enables us to 
generalise equations (1) to solutions in general. The method 
used in the previous paper only needs to be slightly modified. 
Instead of only one, we have to form (r) systems, which we get by 
supposing the solution successively in osmotic equilibrium with 
the r substances 1, 2...r, which, at the temperature considered, 
all are supposed to be in the liquid state. Moreover, we must 
assume that in the state of equilibrium the pressure in the solu- 
tion is the same for all osmotic systems. 

Using the same way of reasoning as before*, we get 

^^^^ ?=Ad^s)pdx = V'-P^Pdp)dx' 

i= 1, 2 ... r. 

dU dc 

^— and -7-^ mean here the variation of U and c per unit length 

ax dx r & 

* Phil. Mag. [6] 13, pp. 607, 608. 

290 Mr Vegard, On some general Properties, etc. 

from a point on the surface of the membrane and along some 
direction in this surface, but as the direction of the surface is quite 
arbitrary, the increment dx may have any direction whatever. 
From equation (32) we get 

^ = 1-Piqi. 

Putting the vahie for ^ into (85) 

(36) *i'' - (^'^\ — ^ = n - ■) — 
s=i pi^dcjpdx ^ ^^ dx 

^■ = l, 2...r. 

If we transform this system of (?') linear equations by means of 
equation (33) we get the result expressed in equation (25), show- 
ing that the osmotic method leads to the same result as that in 
which we used the thermodynamic potentials. 

There is, however, one difference between the two solutions of 
the problem. In order to apply the osmotic pressure method, we 
had to assume that the r components were in a liquid state ; the 
treatment with thermodynamic potentials only requires that the 
solution is fluid at the temperature considered, and the components 
may have any aggregate form whatever. 

§ 10. Summary of results. 

(1) Applying the general thermodynamic equilibrium condi- 
tion, the variation of concentration caused by any field of gravity 
is found for a solution containing any number of substances, and 
the result is expressed in terms of thermodynamic potentials. 

(2) The conception of osmotic pressure is extended to a solu- 
tion containing any number of substances. 

(3) Simple expressions in terms of thermodynamic potentials 
are found for the partial osmotic pressure and for the osmotic 
pressure of the first order. 

(4) By means of the osmotic pressure of the first order we ob- 
tained a physical interpretation of the thermodynamic quantities 

f^. From their connection with the thermodynamic potentials a 

reciprocal relation was found for the osmotic pressure of the first 

(5) The osmotic pressure of the first order gave us a simple 
way of finding the influence of gravity upon a solution. 


THE SESSION 1908—1909. 


October 2Qth, 1908. 

In the Optical Lecture Room. 

Dr Hobson, President, in the Chair. 
The following were elected officers for the ensuing year : 

President : 
Prof. Sedgwick. 
Vice-Presidents : 

Mr S. Ruhemann. 
Prof. Thomson. 
Dr Hobson. 

Treasurer : 
Mr H. F. Newall. 

Secretaries : 

Mr A. E. Shipley. 
Dr Barnes. 
Mr A. Wood. 

Other Members of the Council : 

Mr F. G. Hopkins. 

Mr A. Harker. 

Prof. Larmor. 

Dr Duckworth. 

Mr W. G. Fearnsides. 

Dr Sell. 

Mr W. E. Dixon. 

Prof. Wood. 

Prof. Hopkinson. 

Prof. Seward. 

Dr Fenton. 

Mr (J. H. Hardy. 

292 Proceedings at the Meetings. 

The following was elected a Fellow of the Society : 
G. K Watson, B.A., Trinity College. 

The following Communications were made : 

1. Note on Russo's attempt to show differentiation of sex in the 
ovarian ova of the Rabbit. By W. Heape, M.A., Trinity College. 

2. A further note on the eggs of the hermaphrodite Angiostomum 
nigrovenosum. By S. A. M^'Dowall, M.A., Trinity College. 

3. Plemelj's Canonical Form. By J. Mercer, B. A., Trinity College. 

4. On Monotone Sequences of Continuous Functions. By Dr 

5. The Operator Reciprocants of Sylvester's Theory of Recipro- 
cants. By Major P. A. MacMahon. 

November 9th, 1908. 

In the Cavendish Laboratory. 

Professor Sedgwick, President, in the Chair. 

The following were elected Fellows of the Society : 

J. Pope, M.A., Professor of Chemistry. 
A. Henry, M.A., Reader in Forestry. 

The following Communications were made : 

1. The positive ions given out by hot wires. By Professor 

2. The weight of a corpuscle on the electrical theory of gravitation. 
By Professor Thomson. 

3. Note on the distribution of electric force along the striated 
discharge. By Professor Thomson. 

4. Note on the Radio-activity of Rhubidium. By N. R. Campbell, 
M.A., Trinity College. 

5. The free pressure under osmosis. By L. Yegard. (Communi- 
cated by Professor Thomson.) 

6. The Laws of Mobility and Diflfusion of the Ions formed in 
Gaseous Media. By E. M. Wellisch, (Communicated by Professor 

Proceedings at the Meetings. 293 

'.November 23rd, 1908. 
In the New Medical Schools. 

Professor Sedgwick, President, in the Chair. 

The following were elected Fellows of the Society : 

Y. H. Mottrara, M.A., Trinity College. 
G. R. Mines, B.A., Sidney Sussex College. 

The following Communications were made : 

1. The relationship between human and bovine tuberculosis. By 
Professor Woodhead. 

2. The transmission of Trypanosoma lewisi by fleas and lice. By 
Professor JSTuttall. 

3. The presence of anticoagulin in the salivary glands of Argas 
persicus. By Professor Nuttall. 

4. The mode of action of specific substances. By W. E. Dixon, 
M.A., Downing College, and P. Hamill, B.A., Trinity College. 

5. The action of specific substances in toxaemia. By W. E. Dixon, 
M.A., Downing College, and W. H. Harvey, B.A., Christ's College. 

6. Therapeutic Inoculation for generalised bacterial infections. 
By L. Noon, M.A., Trinity College. 

7. A simple method for examining leucocytes. By C. Ponder, 
M.A., Emmanuel College. 

8. The mode of growth of bacteria. By Dr Graham-Smith. 

9. The radiation of neon in a strong magnetic field. By J. E. 
Purvis, M.A., St John's College. 

10. On the effect of Pressure on the ionization produced by 
Bontgen Rays in different gases and vapours. By J. A. Crowther, 
B.A., St John's College. 

11. On the variation of the relative ionization produced by 
Rijntgen Rays in different gases with the hardness of the rays. By 
J. A. Crowther, B.A., St John's College. 

12. Waves in a stream of viscous liquid. By W. J. Harrison, 
M.A., Clare College. 

January 25th, 1909. 
In the Cavendish Laboratory. 
Professor Sir J. J. Thomson, Yice-President, in the Chair, 
The following was elected a Fellow of the Society : 

J. E. Littlewood, B.A,, Trinity College. 

294 Proceedings at the Meetings. 

The following Communications were made : 

1. A String Electroscope. By T. H. Laby, B.A., Emmanuel 

2. Secondary Rontgen Radiation. By J, A. Crowther, B.A., 
St John's College. (Communicated by Professor Sir J. J. Thomson.) 

3. Interference Fringes with Feeble Light. By G. I. Taylor, B. A., 
Trinity College. (Communicated by Professor Sir J. J. Thomson.) 

4. The solution of Linear Differential Equations by means of 
Definite Integrals. By H. Bateman, M.A., Trinity College. 

February 8th, 1909. 
In the Chemical Laboratory. 

Mr S. Ruhemann, Vice-President, in the Chair. 
The following were elected Fellows of the Society : 

W. L. Balls, M.A., St John's College. 
W. H. Harvey, B.A., Christ's College. 
H. 0. Haslam, M.B., Gonville and Caius College. 

The following Communications were made : 

1. Further studies on Dihydroxymaleic Acid. By Dr Fenton 
and W. A. R. Wilks, B.A., Gonville and Caius College. 

2. Homologues of Furfural. By Dr Fenton and F. Robinson, 
B.A., Peterhouse. 

3. Action of Urethane on Esters of Organic Acids and Mustard 
Oils. By S. Ruhemann, M.A., Gonville and Caius College, and J. G. 

4. The absorption spectrum of a solid alkyl derivative of picene. 
By Miss A. Homer and J. E. Purvis, M.A., St John's College. 

5. The absorption spectra of mesitylene and 3-chloromesitylene. 
By J. E. Purvis, M.A., St John's College, 

6. The absorption spectra of concentrated and diluted solutions 
of chlorophyll. By J. E. Purvis, M.A., St John's College. 

7. A coloured thio-oxalate. By H. O. Jones, M.A., Clare College, 
and H. S. Tasker, B.A., Emmanuel College. 

8. Note on some double Fluorides of Sodium. By W. A. R. 
Wilks, B.A., Gonville and Caius College. (Communicated by Dr 

9. On a configuration of twenty-seven hyper-planes in four dimen- 
sional spaces. By W. Burnside, M.A., Pembroke College. 

Proceedings at the Meetings. 295 

February 22nd, 1909. 

In the Optical Lecture Room. 

Professor Sedgwick, President, in the Chair. 

The following were elected Fellows of the Society : 

J. A. Crowther, B.A., St John's College. 

H. H. Paine, B.A., Trinity College. 

F. Shillington Scales, M.A., Jesus College. 

The following Communications were made : 

1. On the alleged influence of lecithin on the determination of 
sex in rabbits. By R. C. Punnett, M.A., Gonville and Caius College. 

2. Observations on the Changes in the Common Shore Crab 
caused by Sacculina. By F. A. Potts, M.A., Trinity Hall. 

3. On a so-called " sexual " method of forming spores in Bacteria. 
By 0. C. DoBELL, B.A, Trinity College. 

4. On the migration of the thread cells of Moerisia. By C. L. 
BouLENGBR, B.A., King's College, 

5. A note on a specimen of Pelagothuria from the Seychelles. 
By J. C. Simpson. (Communicated by Professor Sedgwick.) 

6. The Study of Discontinuous Phenomena. By N. R. Campbell, 
M.A., Trinity College. 

March 8th, 1909. 

In the Optical Lecture Room. 

Professor Sedgwick, President, in the Chair. 
The following was elected a Fellow of the Society : 
G. Dixon, M.A., Trinity College. 

The following Communications were made : 

1. On the Nature of Anthocyanin. By Miss M. Wheldale. 
(Communicated by Professor Bateson.) 

2. An Experiment on lonisation with y Rays. By L. Vegard. 
(Communicated by Professor Sir J. J. Thomson.) 

3. The Nature of the lonisation produced in a Gas by y Rays. 
By R. D. Kleeman, B.A. (Communicated by Professor Sir J, J. 

4. On Uniform Oscillation. By Dr Young. 

296 Proceedings at the Meetings. 

5. On the parametric I'epresentation of the co-ordinates of points 
on a cube surface in space of four dimensions. By H. W. Richmond, 
M.A., King's College. 

6. The irreducible concomitants of two quadratics in n a ariables. 
By H. W. TuKXBULL, B.A. (Communicated by Dr Barnes.) 

Mai/ onl 1909. 
In the Botany School. 

Dr Hobsox, Yice-Pbesident, in the Chaik. 
The following Communications were made : 

1. On a specimen of the cone Calamostachys hinneyaxa Oarruthers. 
By H. H. Thomas, B.A., Downing College. (Communicated by 
Mr E. A. N. Arber.) 

2. Note on two new leeches from Ceylon. By W. A. Harding, 
M.A., Peterhouse. 

3. I^Tote on an abnormal pair of appendages in Lithobius. By 
L. DoNCASTER, M.A., King's College. 

Jr. On a property of summable functions. By Dr A. C. Dixon. 

Maij 17 th, 1909. 
In the Cavendish Laboratory. 
Professor Sir J. J. Thomson, Vice-President, in the Chair. 

The following Communications were made : 

1. Phenomena of X-ray Transmission. By C. G. Bakkla, M.A., 
King's College. (Communicated by Professor Sir J. J. Thomson.) 

2. Phenomena of the Cathode Discharge. By J. A. Orange, B.A., 
Trinity College. (Communicated by Professor Sir J. J. Thomson.) 

3. Some fatigue effects of the Cathode in a dischax'ge tube. By 
R. Whiddington, B.A., St John's College. (Commimicated by Pro- 
fessor Sir J. J. Thomson.) 

-1:. The intiuence of dilution on the color and the absorption 
spectra of various permanganates. By J. E. Purvis, M.A., St John's 

5. Note on the Histology of the ' Giant ' and ordinary Forms of 
Frimula sinens^i^. By R. P. Gregory, M.A., St John's College. 



Sa7ne fatigue effects of the cathode in a discharge tube. By R. Whid- 

DINGTON. (Communicated by Professor Sir J. J. Thomson) . , 183 
^ote on the electrical behaviour of fluorescing iodine vapour. By E. 

Whiddington. (Communicated by Professor Sir J. J Thomson) . 189 
On the Reflection of Sound at a Paraboloid. By the Rev. H. J. 

Sharfe , . .190 

Discussion of a difference equation relating to the tension of overhead 

wires supported by equidistant poles. By A. A. Robb . .. . 198 
On a property of summable functions. By A. C. Dixon . . . 210 
On certain phenomena of the kathode region. By J. A. Orange. (Com- 
municated by Professor Sir J. J. Thomson). (Plates IV— IX) . 217 
Note on two new Leeches from Geylon. By W. A. Harding . . . 233 
Note on the ahnormal pair of appendages in Lithobius. By F. G. 

Sinclair 235 

On a specimen of the cone Calamostachys binueyana (fjarr.). By H, 

Hamshaw Thomas. (Communicated by Mr E. A. Newell 

Arber) 236 

Note on the Histology of the Giant and Ordinary Fornix of Primula 

sinensis. By R. P. Gregory. (Plate X) 239 

The influence of dilution on the colour and the absorption spectra of 

various permanganates. By J. E. Purvis. (Plate XI) . . . 247 
Phenomena of X-Ray Trarismission. (Preliminary Paper.) By C. G. 

Barkla. (Communicated by Professor Sir J. J. Thomson) . . 257 
The Emission of Rontgen Rays from Thin Metallic Sheets. By G. W. C. 

Kate. (Communicated by Professor Sir J. J. Thomson) . . 269 
On the Scattering of the ^-rays from Radnmi by Air. (Preliminary 

Note.) By J, A. Crowther . 273 

On some general Properties of Mixed Solutions. By L. Vegard . . 275 

Proceedings at the Meetings held during the Session 1908 — 1909 . 291 





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Camkitrgt ^j^ilaisapl^kal ^^omtg. 

On the Oscillations of Superposed Fluids. By H. J. Priestley, 
M.A. [Communicated by W. Welsh, M.A.] 

[Received 28 October 1909.] 

[Read 8 November 1909.] 

In his classical research "On the Theory of Oscillatory Waves" 
Stokes* has shewn that the first order period equation for waves 
at the free surface of a liquid is modified when we take into 
consideration the third order terms. The present paper is under- 
taken with the object of finding the corresponding modification 
for waves at the common surface of two fluids ; and ascertaining 
the effect of the small terms on the stability when the upper 
fluid has a stream velocity. It is found that the range of wave 
lengths for which oscillations are possible is greater than that 
given by the first order equation. When the upper fluid has no 
stream velocity the period given by this equation is too long 
in the case of propagated waves and too short in the case of 
standing waves. 

For the propagated waves the method adopted is a modification 
of that used by Stokes in his Supplementf to the paper quoted 
above. This method is found unsuitable for the standing waves, 
and it is necessary to use direct approximations from the ordinary 
equations of motion. In each case the origin is taken in the 
undisturbed surface, with the axis of y vertically upwards. The 
sign given to the velocity potential is that adopted by Professor 

Lamb, so that the velocity along the x axis is — ^ , 

* Math, and Pliijs. Papers, Tome i. pp. 197 et seq. 
t Ibid. pp. 317 et seq. 

VOL. XV. PT. IV. 20 

298 Mr Priestley, On the Oscillations of Superposed Fluids. 

I. Propagated Waves. 

Reducing the problem to one of steady motion by the usual 
artifice we express the coordinates of any point in terms of the 
velocity potential and stream function by means of the equations 

for the lower liquid, and 

«t = 

for the upper. 

Ai, A^, Az ... etc., Bi, B^, B^... etc. are two series of quantities 
in descending order of magnitude. 

The conditions to be satisfied at the common surface are 

Xi + iyi = x^ + Ly^ (3), 

and the pressure condition 

P,I8, + Igp, {y, + CO = p,IS, + ^gp, {y, + G,) (4), 

and Cj and Cg are constants. 

We have yet to choose our origin for -y^ and we select the 
common surface as the line -^^r = 0. 

Writing '^ = (f)/U, condition (3) gives 

We proceed to find relations between the A's and B's from this 

1st Approximation. 

^2 "~ ^1 = * (-Do — -^o), 
whence Aq = Bq] 

and ^1 = ^2] 

We take as the common first approximation to ^1 and ^2 the 
mean of the two exact values which we denote by ^. 

2nd Approximation. 

^^ _ ^, = t {B, - Ao) + (A, + B,) sin A;^ + t{B^- A^) cos k% 

^ = 5, = /3(say)' 
^2 - ^1 = 2/3 sin ^^ I ,g. 

.-. % = ^ + ^smk^f ^ ^' 

^^ = ^-^sinA;^ 

Mr Priestley, On the Oscillations of Superposed Fluids. 299 

3r(^ Approximation. 
%-X = i{B,-A,) + le-'^^ «i^ ^^ [B, e-'^^ - A , e'*^] 

+ I [B.,e-''''^ - A.e'^^^l 
whence we obtain, by equating coefficients of different harmonic 
terms in the imaginary part, 

B,-A,= W^] 

A,-B, = k^A (C), 

A, =B,] 

while the real part gives 

% = ^ + ^smk% + ^ (A, + B,) sin 2^^, 
^1 = ^ - ;8 sin ^^ - -I (^2 + B,) sin 2k^. 
[/3 may now differ from its former value by a small term of 
order A;/3^.] 

4<th Approximation. 

X-%=l{B,-Ao) + ie-'*[^ smk^+i(A,+B,) sm-2k^] [^^g-^fc^ _ A,&''^] 

+ i[Bse-''^^-A,e''^^]. 
Equating coefficients of the different harmonic terms in the 
imaginary part we obtain 

Bo-A, = kl3' ^ 

B,-A, = ^^k(A, + B,) 
B,~A, = -k^' 
B,-A,=^-^^k(A, + B,)) 

Pressure Condition. 

To determine completely the quantities A and B we require 
another set of relations between them. These relations are found 
from the pressure equation (4). To use this equation we must 
find 1/^ in terms of sines and cosines of multiples of ^ and this 
we proceed to do. 

Value of 1/^1. 


From (1) 



where , , , 

Wi = 9i 4- iyi. 

= - [(1 + Ml cos k% + 2k A^ cos 2k% + ...) 
+ L (Ml sin A;^i + 2k A^ sin 2^^i +...)], 
when ^/tj = 0. 

Thus 8^ = Ur" [1 + 2klmA,n cos mk% + k^'S.m'^A,,,^ 
+ 2k^Xm7iAyiAn cos (m — n) k%], 


300 Mr Priestley, On the Oscillations of Superposed Fluids. 

the last summation being taken once for each pair of values 
m and n, 

= U^-' [1 + A-^i- + 2k [A, cos A-^i + . . . + SA, cos SJc%] 

+ 2h-{2A,A,cosk%}l 
neglecting terms of order higher than 1^(3'. 

Expanding ly'>S'i by the Binomial Theorem and neglecting 
terms of order higher than k^^"^ we have 

IIS, = C^i- r 1 _ j^^^A^^ _ 2k [A, cos A-^i + 2^, cos 2A-^i 

+ 3^3 cos 3A;^i} 

+ 4^-2 [A;' cos^ A:^i + 4>A,A., cos A-^i cos 2A;^i} 
+ U-'A,^ cos k% - Sl^A,^ cos* A;^i 

We pass to the corresponding value of 1/aS^2 by changing the 
sign of A; and using B coefficients. 

Since the origin is in the undisturbed surface the pressure 
equation is satisfied over the line y — when there is no wave 
motion. This gives 

p,U,' + 2gpA = P,W + ^gp-2G,. 

Using this condition we obtain the following relations from 
the pressure equation. 

1st Appi'oximation. 

2gp,Ao = 2gp.B„ 
which, with A^y — B^ (equations A), gives 

.4o = 0, 
^0 = 0. 
2nd Approwimation. 
Pi Ui' (- 2A;^i cos Ar^i) + 2gp, (A,, + A, cos A-^i) 

= p.^u/(2kB, cos k%) + 2gp^ (B, + B, cos A;^,)- 
Remembering Ao = Bo, Ai = B, = ^, (B), and 

^1 = ^2, (A), 

this gives A,, = B^ = 0, 

and g (p, - p.^/k = p, LV + p-2 U.f, 

the ordinary period equation*. 

Srd Approximation, 
pi Ut" (- 2A;^i cos A;^i - 4^vl2 cos 2A;^i - t-Ai' + ik^Ai" cos- A-^j) 

+ 2(7/3i [^0 + ^1 cos A;'^i + A. cos 2A-^i] 
= p.,U.i {2kB, cos k% + 4<kB.2 cos 2k%, - k-B^^ + 4^•-5r cos^ k%) 

+ 2gp.^ [Bo + Bi cos k% + B^ cos 2A;^2]. 

* Lamb, Hydrodynamics, § 224, ed. 1895. 

Mr Priestley, On the Oscillations of Superposed Fluids. 301 

Expressing the harmonic terms in terms of "^ instead of ^i and 
^2) and neglecting terms of order Jr/S^' we obtain, by equating 
coefficients of different harmonic terms to zero, 

2 (p,Ao - p,B,) = - (pi + p,) kl3\ 
9 (pi - P2)/k = pi U,' + p, Ui = K, (say), 
p, U,' [3A;2/32 - 4>kA,] + 2gp, [A, - ^k/3'] 
= p,U,' [2k'^ + ^kB,] + 2gp, [B, + ^k^']. 

These equations, combined with (C) above, give 

Bo = W [ m 

A, = kl3'p,U,'IK I ^ ^' 

B, = -k/3^p,U.//KJ 

We note that, as in the case of waves on a free surface, the 
period equation is not changed at this stage of the approximation. 

4<th Approximation. 

In proceeding to the next approximation we adopt the same 
method as before. The period equation is obtained from the 
coefficient of cos k'^ in the reduced pressure condition. This 
coefficient gives 

p, U,^ [- 2kA, -\k'^{A,+ B,) + i/c^yS^j 

+ 2gp, [A, + ik^ (A, + B,) - ^¥^' + k^A,] 
= p,Ui [2kB, - \k^^ {A, + B,) - iP/3^] 

4- 2gp, [B, -ik^(A, + B,)- 1 A;^^^ - k^B,]. 
Remembering that 

gk-'(pi-p2) = PiU^' + p,U,' 
to the order k^ and 

B,-A, = ^^k (A, + B,) = Ik^^^ (p, U,^ - p, Ui)l{p, U,^ + p, Ui), 
we obtain for the period equation 
9k-'{p,-p,)-K=-k'^'{p,'U,* + piV,')l{p,U,' + pJIi)...{b). 
Before discussing this result we proceed to find the wave 
profile. To do this we require the values of the ^'s and jB's to 
the order k"^^^. 

The coefficients of the absolute term and cos 2k'^ in the 
pressure equation are the same as the con-esponding coefficients 
in the third approximation. Hence A^, B^, A^, B^ have values 
already given (E). 

A-i and Bg are found from the coefficient of cos Sk'^, which, 
with the help of (D), gives 

^3 = 1 PiU,' i2p,Ui' - pJJi)K-^^'k\ 
B,= lp,Ui{2p,Ui-p,U,-)K^^%\ 

S02 Mr Priestley, On'the Oscillations of Superposed Fluids. 

Equation (1) gives us the transcendental equation of the free 
surfoce in the form 

X = -%- A^ sin ^-^1 - A. sin 2Jc% - A., sin SA-^i, 
y — A,, + ^1 cos A-'^i 4- A ., cos 2A-^i + A^ cos SA-^i. 
From these we find 

^j = _ X + ^1 sin hv + (^o - ^Auli^) sin Ihx, 
and, using values of coefficients already found, 
y = [A-, + 1^-/33 (4/)i TJ;^K-^ - 1)] cos hx 

+ \h^- (pi U;' - p, U^ K-' cos 2kx 

+ ^Jc'/S'il - 6p, C/i" . p.,U.^ . Z-") cos Skx. 

Writing b for the amplitude of the principal harmonic term 
we have, to order Jc"^'^, 

y=h cos kx + ^Jcb- (pi f/j- — p.. U.f) K~^ cos 2k-x 

+ |M)S [1 - 6pi U^' . p., CTo^ . K-^] cos 3Aw (6). 

Both this equation of the wave profile and the period equation 
reduce to Stokes' equations for waves on a free surface on putting 
P. = 0. 

In discussing these results we shall denote the wave velocity 
by c and the stream velocity of the upper fluid by u, so that 

U^ = — c; U.2= u — c. 

Writing the period equation in the form 

gk-' {p, -p,)-K = - Jc^^-^ [K - 2p, ^r . p. U^ • K-'l 

and remembering that K may be put equal to gk~'^ (pi — p.j) in the 
small terms, we notice that, corresponding to a given wave length, 
the small terms have their greatest importance when U2 = or 
c = w and their least importance when piC/i'' = poC/o'^. 
The first case gives 

c- = gk~^ (1 — s) [1 + k^fi'] , where s = ps/pi. 

Turning to the equation of the wave profile we see that the 
small terms have their greatest importance for this value of c. 

The equation takes the form 

y = h cos kiV + h kb- cos 2kx + ^k^b^ cos Skx, 
which is the form Stokes found for waves on a free surface. The 
expression for the velocity only differs from Stokes' free surface 
velocity by the factor (1 — s). 

The second case gives 

whence c" = ^ gk-' {1 - s) (I + ^k''^) (7), 

and u=±c(l±s^)ls^ (8). 

Mr Priestley, On the Oscillations of Superposed Fluids. 303 

For tbis case the correction to the wave profile has its least 
value. (Note. The correction in the cos ^kx term has not its 
numerically smallest value.) The wave form is given by 

y = h cos kx — r^ k%^ cos ^kx. 

[This wave is traced for the value kh = '5.] 

Thus waves travelling with velocity given by (7) are least 
affected by the small terms. The corresponding stream velocities 
in the upper liquid are given by (8). 

Fig. 1. 

c = [i^fc-i{i-s)]i 

A, wave form as given by first approximation. 

B, wave form corrected for terms of order /c^ft*. 

Stability of waves for a given value of u. The period equa- 
tion is 

Pi U,' + P. Ui = gk-' (p, - p,) + k'^^ ip,' U,^ + pi U,')l(p, U,' + p, Vi). 

In the small term we can take the first order values of c and 
hence that term may be considered a known function of k and u. 
The period equation therefore gives as a quadratic equation for c 

c' (pi + P2) - 2cM/), + p-fw" = gk-^ (p, - p^) + P^2^2, 

where P = {p,^ U,^ + p.^ U,%p, U,^ + p, U,% 

304< Mr Priestley, On the Oscillations of Superposed Fluids. 


c = up-Api + p2) ^ 

± [gk-^ (pi - p,)/{p^ + p-d + PA-^- - it"p,p,l{p, + /3,)"']-. 
Thus c is real if 

gk-' (1 - s)/(l + s) > »"5/(l + sf - PA:-/3-. 
Hence the range of unstable wave lengths is smaller than that 
given by the first order equation and the corrections for small 
terms tend to make the sj'stem more stable. 

As in the first order case the shortest possible wave travels 
with a velocity us/{l + s). 

II. Standing Waves. 

The method of the first part of the paper is unsuitable for the 
discussion of standing waves so we proceed as follows : 

With the origin in the common surface and the y axis vertically 
upwards we assume for the lower liquid 

(f), + if, = -ZA,„e-''''*^'=+'y\ 
and for the upper 

The condition to be satisfied at the common surface is 

pi^i-gpiy-k piQi' = p-2<l>2- gp-2 y-h p-^qi - F (t), 


qi" = k-'Zm-AJ'e''''^J + 2^--27wiJ.„i^„e(»^+»*' ^'J cos {m - n) hx 
= k"Ai- (1 + '2ky) + 4^^^i-42 cos kx 

(to third power of the amplitude), 

and F (t) is a function of the time. 

This condition gives the equation of the common surface 
Avhich we will write 

The condition that no part of either liquid shall floAV across the 
common surface leads to the equations 


dt ^ dx ^ dy 

dU dU dU^^ 

dt ' dx '^ dy 
where {uy, v^), (u^, v,,) are the x and y components of the velocities 
in the two liquids. 

We proceed to find the values of the ^'s and B's by successive 
approximations from the conditions (1). 

Mr Priestley, On the Oscillations of Superposed Fluids. 305 

1st Approximation. 

The equation of the free surface is 

(J (p, - p^)y=(piAi- P2B1) cos kx + F(t). 
The origin being taken in the undisturbed surface, we have 
F(t) = and 

g (pi -p2)y = (pi^i - P2-B1) cos kx. 
The surface conditions give 

Pi 4.1 ~ P2^i + 9iPi- P2) kA^ = 0, 

PiAi - pA -9 {pi- P2) kB, = 0, 
Avhence Ai = — Bi= p^k~'^ sin pt, (say), 

and p^ = gk{l — s)/(l + s), where s = p^jpi. 

Using the values of A^ and Bi, we have, as equation of the 

y = ^ cos pt cos kx. 

2nd Approximation. 
The equation of the free surface is 
g {p-i — p2)y = Pi^i (1 + ky) cos kx — p^B^ (1 — ky) cos kx 

-!- P1A2 cos 2kx — P2B2 cos 2kx 
-lp,k'A,' + ^P2k'B^ + F{t); 
whence, using first approximations to Aj, B^ and y in the small 
g (pi - p2)y = (pi-^i - P2B1) cos kx + {P1A2 - P2B2) cos 2kx 

+ (pi — P2) p^^^ cos^ pt cos^ kx 
- ^{pi-p2)p'/3' sin' pt + F{t). 
The velocities, required for the surface conditions, are given by 

Wi = — ;^ = ^^1 sin kx, (to first order), 


Vi = — -^ = — kAi cos kx (1 + ky) — 2k A^ cos 2kx 


= — kAi cos kx — 2k A^ cos 2kx 

— pk^' sin pt cos pt cos^ A;a;, (to second order), 
with similar values of U2 and v^. 
The surface conditions give 

(/3j j-i — P2B1) cos A;i» + (pi^2 — ^2-^2) cos 2kx 

— (pi — P2) i'^/S^ sin 2pt cos^ ^ic 
-HPi-P2)p^/3^sin2pi + i?"(0 

— (pi + P2) p^/3^ sin^ kx sin p^ cos^i 

+ (/ (pi — P2) [kAi cos Z?^ + 2kA2 cos 2A;a; 

+ A>p/3" cos kx COS pt sinp^] = 0, 
with a similar equation from the other liquid. 

306 Mr Priestley, On the Oscillations of Superposed Fluids. 

Equating the coefficients of the absolute term, cos kx and 
cos 2kx to zero in these two equations, we have the following sets 
of relations : 

F'(t)-{p,-p,)p'fi'sm2pt = (2), 

(from both equations), 

Piii - p^Bj +9 (pi- P2) kA^ = 0] 


PiAi-p.B^-g(pi- p,)kB^ = Ol 

p,A, - pA + 2i?^ (pi + p.^ A, = - p,p'^' sin 2pt] 

p^ A, - pA - 2p' (pi + P2) B, = p,p'/3'^ sin 2pt\ '^ ^' 

(on making use of the period equation to eliminate g). 

From (3) we see that Ai is still equal to — Bi] we shall still 
give them the value p^k~^ ^inpt. The period equation will be the 
same as before. 

From (4) A^ = - ^p./ipi + p^) p^' sin 2pt, 

-B2 = - ipi/(Pi + p2)p^' sin 2pt, 
and from (2) 

F(t) = - Hpi - P2)f^' COS 2pt + C, 
where (7 is a constant of integration. 

To keep the origin in the undisturbed surface we take (7 = 0. 
The equation of the surface takes the form 

y = (3 cos pt cos kx + \k^^ (1 — s)/(l + s) cos^ pt cos 2kx. 
Srd Approximation. 

9 (pi - p2)y = Pi4i (1 + % + i^'2/') cos kx 

— P2B1 (1 —ky + ^k^y'^) cos kx 
+ pi Jia (1 + '^ky) cos 2kx 

— p^B^i^. — ^ky) cos 2kx 
+ (piAs - P2-B3) cos Skx 

— ipiA;2 [^1^ (1 + 2ky) + 4^.1^2 cos kx] 
+ ^p2k^ W (1 - 2%) + 4<B,B^ cos kx] 
+ F(t). 

On using above values for y, A's and B's in the small terms 
and writing 

X(t) = F{t) + UPi-P^)P'^'^^^^pt> 
this becomes 
9 (pi - P2) 2/ = % (0 + cos kx [pi^i - pa^i] + cos 2kx [p^A^ - p^B^ 
+ cos ^kx [pi J.3 — P2-B3] + 1- (pi — P2) p^^"" cos 2kx cos^ pt 

,cx<^ + (7p,^ + 7p,^ - 10p,p3) cos ptl 

4- COS Skx \^^P'' + ^^^' - ^"^P'P^^ '^' ^^^ 
- 1 +(9p,^+ 9p,^-38p,p2)cos_p«. 

+ ^V^PW(P: + /^0 

. - - ^^ = 


Mr Priestley, On the Oscillations of Superposed Fluids. 307 

To apply surface conditions (1) we shall require the 
^i- velocities to the second order and the y- velocities to the third 

These are given by 

Ui = — -— = kA^ sin kx (1 + ky) + 2k A^ sin 2kx 
= kA-i^ sin kx 4- '2k A ^ sin 2kx 
+ kp^- sin kx cos kx ^mpt cos pt, 

kA^ cos kx {1 + ky + \k^y^) 

— 2k A^ cos 2kx (1 + 2ky) 

— SkAs cos Skx 

= — kAi cos kx — 2k A 2 cos 2kx — 3 A; J. 3 cos Skx 

— pk^^ sin ^^ cos pt cos" A;« 

— ^pk^^^/{pi + P2) • cos^^i sin_p^ [{^Ri — ^^Rz) cos ^a; 

+ (3pi- 17/32) cos 3Ar«], 
with similar values for u^ and ■Vg. 

Writing these values in the surface conditions (1), using 
known approximations to coefficients wherever possible and 
eliminating g by means of the period equation in all terms 
except those of the first order, we obtain the following sets of 
relations : 

%'(0 = (5), 

piAi - p^B^ + 9 {pi- P2) kA^ 

"(40/31^ + 44/J2' - 132pi|02) sin 3pf 
' |_ + ( Spi^ + 1 2 pi - 4/9i Pa) sin pt_ 

Ri-Ai - p^B^ -gipi- P2) kB^ 

'(44pi2 + 40p/ - 132pip2) sin 3^^ 
' L + {12 p{- + Spi - 4|Oi/32) sin pt_ 


p^A^ - p^B^ + 2^2 (pi + /92) ^2 = - p^y^'' sill 2^^) 
Pii; - pA - 2p' (pi + p,) B, = /9i_p^/3^ sin 2pt] 
PiA,-p,B, + Sp'{p^ + po)A, 

{21pi — 9^2) sin Spt 

^kp'^'Kpi + R2) 

= i,kfmp, + p,) 


= - ^kp'^%/{p, + p,) 

pJ,-pA-^pHri + p2)B, 

= -^kp'^'p,l{p, + p,) 

_ +{5p^-9p2)sinpt 

"(21^2 — 9/Ji) sin Spt 
+ {5p2- 9 pi) sin pt 

308 Mr Priestley, On the Oscillations of Superposed Fluids. 

(5) and (7) shew that F{t), A^, B^ are not changed by this 
closer approximation. 
If we write 

4i= p/3^~i sinj9^ + Ci, 
B^= — p^k~^ sin pt — A> 
we obtain, from (6), 

G^-D^ = - ^pk^' (p, - p^)/(p, + p,) . (sin pt + sin Spt). 
The part of Gi and D^ depending on sin pt is indeterminate as 
any addition to that part simply means a change in the amplitude 
of the principal oscillation. 
We take 

C\ = ^pk^^pj(pi + p.2) . sin pt + C^ sin Spt, 
Di = ^pk/3^pi/{pi -r P2) ■ sin pt + A sin 3^^. 
If we use these values in the two equations (6) and equate the 
coefficients of sin pt and sin Spt to zero we have four equations. 
Two of these are the same and lead to the new period equation, 

p^ =gk{l- s)l{\ + 5) . [1 - P^yg^ (1 + sO/(l + sf] (9), 

the other two give equations for G.^ and Do, the solutions of 
which are 

C^2 = - i-^pk^' (5pi^ + pi - 12p,p,)/{p, + p,y . sin 3^^, 
A = - ^pkl3' {pi + 5pi - 12p,p,)l(p, + p,y . sin Spt 
Equations (8) give 
As/pk^^ = ip^ (3p2 - pi)l(pi + p^y sin Spt 

+ T6P2 (9p2 - 5pi)/(/Ji + pif sin pt, 
Bs/pk^^ = - ipi (3/Ji - p2)/(pi + pif sin Spt 

- 16 Pi i^Pi - ^p2)/(pi + P2)' sin pt. 
If we now denote the amplitude of the principal oscillation 
by h we find for the equation of the wave profile 

y = [b cos pt — ■^k'^lf (pi + pi)l{pi + p^y . cos Spt] cos kx 

+ — (/?!- p2)/(pi + P2) cos^ pt cos 2kx 

+ ^k""})^ (/3i - S/J2) {Spx - p2)Kpi + pif cos^ pt cos Skx . . .(10). 

Comparison with propagated wave. 

Wave Profile. 

Putting ti = in equation (6) of section I we obtain, as the 
equation of the profile of the propagated wave when the upper 
liquid has no stream velocity 

y = h cos kx + ^kb^ (p^ — p2)/(pi + P2) • cos 2kx 

+ %k''h' {pi + pi - ^pipi)l{pi + pif cos Skx. 

Mr Priestley, On the Oscillations of Superposed Fluids. 309 

Comparing this with the standing wave given by (10) [section II] 
we see that the forms of the propagated and standing waves 
are the same if we neglect the second power of the ratio of the 
amplitude to the wave length but are different if we proceed to 
a higher approximation. 


We have seen that the period equations are not altered by 
terms of order k^. When we proceed to the next approximation 
the period of the standing wave is given by (9) [section II] while 
that of the propagated wave is found from 

p2 = gk{l- s)/(l + s) [1 + k'^' (1 + sO/(l + s)'] 
[(5) section I]. 

We see that the period 2'7r/p given by the first order equation 
is too long for the propagated waves and too short for the standing 
ones. We proceed to tabulate the periods for waves of length 
10 ft. and 100 ft. We take 

k^ = "5 and g = 3216 f.s.s. 


10 feet 

100 feet 

1st order 



1st order 

























































310 Mr Campbell, Discontinuities in Light Emission. 

Discontinuities in Light Emission. By Norman Campbell, 
M.A., Trinity College. 

[Bead 8 November 1909.] 


1. Introduction. 

2. The ideas underlying the experiments. 

3. 4. The theory of the method of experiment. 
5. General nature of the experiments. 

6 — 10. Mathematical theory of the interpretation of the observations. 
11 — 15. The apparatus : 

11. The source of light. 

12. The photo-electric cells. 

13. The measuring instruments. 

14. The high resistance. 

15. Measurement of the instrumental constants. 

16. Numerical calculations showing the possibility of the experiment. 

17. Combination of the observations. 

18 — 20. The experimental difficulties which have prevented the at- 
tainment of results. 

§ 1. The following pages are the account of an experiment 
which failed. The occasional publication of a description of such 
failures may be justified by two reasons, both of which appear to 
me sufficient in the present case. In the first place, the theory of 
the experiment may be of interest : and, according to the view 
which is taken of the causes of failure, others better equipped for 
the task may be induced to repeat the attempt, or others, to whom 
the same idea may occur, may be saved from wasting their time. 
In the second place, the methods of experiment, if they are novel, 
though unsuccessful in their immediate object, may have other 

§ 2. The ideas on which the experiment was based are not 
easy to describe in a brief title : a little explanation is needed. 

According to all modern theories of radiation, the emission of 
light is discontinuous in time. Whatever may be the nature of 
the radiators from which the light proceeds, there is little doubt 
that their vibration is not continuous. They are set into vibration 
by some external disturbance, such as the impact of electrons, and 
continue vibrating until the energy so acquired is dissipated by 
the damping due to radiation : they are then quiescent until the 
occurrence of a fresh disturbance. 

But there are at least two theories of radiation which suggest 
that light emission is discontinuous in space as well as in time. 

Mr Campbell, Discontinuities in Light Emission. 311 

These theories were proposed by J. J. Thomson* and by Planck •}-. 
They both suggest (at least if we interpret Planck's theory in the 
sense given to it by Stark :]:) that the light from a single radiator 
is not emitted equally in all directions, but is concentrated along 
a finite number of narrow tubes radiating from the radiator : they 
also suggest that the energy emitted by such a radiator in virtue 
of a single disturbance is not infinitely divisible, but only divisible 
into a finite number of equal parcels, the magnitude of which, 
according to Planck, depends on the frequency : further, this finite 
number is usually quite small under experimental conditions. 

This view is capable of explaining many difficulties connected 
with the ionisation of gases and allied phenomena which are 
quite incomprehensible on the older theory that the light spreads 
out from the radiator as a spherical wave. But it also raises some 
new difficulties in connection with optical interference. If the 
light from a single radiator can only be split into a small number 
of parts, then, if the beam of light from an ordinary source, con- 
taining a great number of separate radiators, is divided by any of 
the ordinary interference methods, the light in one beam must, in 
general, come from radiators different from those which emit the 
light in the other. Two rays of light which come from different 
radiators will be termed ' independent.' 

And hei'e a distinction, which may be of importance for oar 
purpose, must be made between the two methods of exciting inter- 
ference. In the first method, of which Fresnel's mirrors are 
typical, the two beams which are made to interfere eventually 
are emitted at different angles from the source: they will be 
independent, in our present sense, if it be true that the light 
from a single radiator is emitted in one direction only, and 
this conclusion requires no assumptions as to the divisibility of 
the energy in the light from a single radiator. In the second 
method, exemplified by Michelson's interferometer, the two beams 
proceed from the source in the same direction. They will be 
independent, only if it is impossible to split up the energy from a 
single radiator into two parts, so that the beam reflected by the 
half-silvered mirror must come from different radiators from that 
transmitted by it. On Planck's theory of radiation there should 
be no distinction important for our purpose between the two 
interference methods, but on Thomson's theory it is possible that 
the two beams produced by the second method are dependent, 
while those produced by the first are independent. 

Now it is not difficult to imagine why two independent beams 

* See Electricity and Matter, London, 1904, p. 63, or Proc. Camb. Phil. Soc. xiv. 
1907, p. 417. 

t M. Planck, Wdrmestrahlung , Leipzig, 1906. 
J J. Stark, Phijs. Zeit. x. 1909, p. 579. 

312 Mr Campbell, Discontinuities in Light Emission. 

should show interference, but it is difficult to explain why two 
beams should interfere when they come originally from a ' single 
source/ and should not interfere when they come originally from 
' different sources.' For, on this view, in both cases they really 
come from different radiators. Accordingly it appeared that con- 
siderable value would attach to any experiment which should 
indicate, by means of observations other than those of optical 
interference, whether the two beams, into which a beam from a 
single source of light is divided by interference methods, are to be 
regarded as coming from the same or from different radiators. 

§ 3. Now the theory recently given by Schweidler*, and applied 
to radioactive processes by Kohlrauschf, by Meyer and Regenerj, 
and by Geiger§, provides a very powerful method of investigating 
any discontinuous process. Schweidler showed that if any effect, 
of which the magnitude can be measured, is due to the random 
occurrence of a finite number of independent events, then the 
magnitude of the effect will not be constant, but will show fluctua- 
tions about a mean value, and that from the magnitude of the 
fluctuations the number of independent events can be calculated. 
Further, if the magnitude of the sum or difference of two effects 
so constituted is measured, the square of the mean fluctuation of 
the sum or difference is the sura of the squares of the mean 
fluctuations of the two effects, if, and only if, the events which 
constitute one event are wholly independent of those which 
constitute the other. If, on the other hand, there is complete 
correlation between the events constituting the two effects, the 
mean fluctuation of the difference will be zero. In a recent 
paper II , which will be quoted frequently below, I have en- 
deavoured to investigate closely the application of this theory to 

§ 4. Suppose, then, that by some means we can measure the 
intensity of a beam of light in such a way that the total intensity is 
the sum of the intensities of the radiations' from the isolated radia- 
tors of which the source is composed. Let us split up the beam from 
a ' single source ' by one of the ordinary interference methods and 
measure in this way the difference in the intensity of the resulting 
beams, adjusting the arrangements so that the mean difference is 
zero. If the older theory of radiation is correct, there is complete 
correlation between the ' events ' which constitute the two beams : 
when a radiator sends light into one beam, it also sends it into 
the other. But if the newer theory of the radiation is correct, 

* Schweidler, Congres Internal, a Liege, 1904. 

t Kohlrausch, Wien. Ber. 1906, p. 673. 

J Meyer and Eegener, An. Ph. xxv. p. 757. 

§ Geiger, Phil. Mag. April 1908, p. 539. 

II Campbell, Proc. Camb. Phil. Soc. xv. 1909, p. 117. 

Mr Gamphell, Discontinuities in Light Emission. 313 

the 'events' are independent, or very nearly so, for in general each 
radiator sends its radiation into one beam and not into both. On 
the first theory the mean fluctuation of the difference should be 
zero: on the second the square of the mean fluctuation should 
be the sum of the squares of the fluctuations of either beam 

§ 5. The application of these ideas to experiment was 
attempted in the following way. The intensity of the beams 
was measured by means of the photo-electric current which they 
excite in the alloy of sodium and potassium in a high vacuum. 
It seems reasonable at the outset to suppose that each train of 
radiation emitted by a single radiator, when it falls on the alloy, 
liberates a number of electrons which is, on the average, the same 
for all radiators and independent of the total intensity of the 
beam, i.e. the number of such trains emitted in a given time. If 
this assumption be true, then the difference between the photo- 
electric currents due to the two beams will be a function of the 
difference in the number of trains of radiation constituting the 
two beams, and measurements of the fluctuations of this difference 
will enable information to be deduced as to the independence of 
these trains. The fluctuations were measured by Meyer and 
Regener's method of observing the readings of an electrometer, 
the quadrants of which were connected to the two ends of a high 
resistance through which the current passed. 

§ 6. Before proceeding to detail the experimental methods it 
will be well to consider the theory a little more closely : if this 
order had been adopted in the first instance much time would 
have been saved. 

The main result of the previous paper* may be stated as 
follows. Let Xt be the average number of events which happen 
in a small time t, and let x be the deviation of that number 
from its mean value during the time r : let 

0=f{t) (1) 

represent the motion of the indicator of the measuring instrument 
at alHnmes t subsequent to the happening of one of the events, 
and drp'^ the square of the mean deviation of the indicator from 
its mean position for all times T from the moment of starting the 
observations, where T is a time long' compared with the time 
constants of the measuring instrument. Then it is shown that 

eT"=a;'/T.I f'(t)dt (2). 


§ 7. We have first to calculate x^. The ' events ' in our case 
are the liberation of individual electrons. Our fundamental 

* Campbell, loc. cit. 
VOL. XV. PT. IV. 21 

314 Mr Campbell, Discontinuities in Light Emission. 

assumption states that the number of electrons liberated is pro- 
portional (at any rate for a given intensity of the light) to the 
number of light disturbances falling on the cell. If N is the 
average number of such disturbances striking the cell in unit 
time, ft) the average number of electrons liberated by each light 
disturbance, then 

Xt = Ncot (3). 

The fluctuations of X, which are measured by x^ arise (1) from 
fluctuations of N and (2) from fluctuations in co. The introduc- 
tion of ft) allows for all changes of the absorption of the light in 
different parts of the optical train, and for all differences in the 
state of the cell and the manner of the incidence of the light 
upon it. Then, if f and i] are the deviations of Nt and oo respec- 
tively from their mean values during any very short time r, we have 

(Xt + x) = {Nt+^)(co + v) (4), 

and OS = Nrr] + ^Q) + ^7] (5), 

and "^ = [N^'t)^ + f ft,2 + |2^2 + 2Nt7]^co + Wrrf^ + ^^wrj] . . .(6). 

It will be assumed that ^ and rj are wholly independent, hence 
V^> ff^ ^^d ^'rf are all zero, since t) and f are zero. Also, since 
T tends to the limit zero, NH'^ is infinitesimal compared to a. 

Therefore ^=P(w2-|-7f) (7). 

As was proved in the previous paper, 

J^ = Nt .....(8). 

Hence '^- = N {w'' + t)'') r (9). 

§ 8. (9) gives the result when we are considering a single 
beam falling on a single cell and measuring the fluctuations of 
that cell as Meyer and Regener* measured the fluctuations of a 
single source of a rays. Let us now consider a second cell (the 
quantities referring to which are distinguished by dashes) and 
measure the fluctuations in the quantity X — X', where X = X'. 
In this case t) and 77' are independent and it will be assumed that 
^2 _ ^'2. ^ g^^(j ^' QTj-Q dependent or independent according as the 
two beams of light are dependent or independent in the sense 
which has been discussed. Then it is easy to show that, if x 
now represents the fluctuations in {X — X')t, 

x'=2N{co' + ^')t (10) 

if the beams are independent, or 

-'^"=2N^'t (10') 

if the beams are dependent. 

* Meyer and Eegener, loc. cit. 

Mr Campbell, Discontinuities in Light Emission. 315 

§ 9, We cannot estimate the value of 7f until we know (and 
we are not likely to know in the near future) the causes of the 
fluctuations of w. But, from the general theory of probability, it 

is certain that -^ will diminish as co increases. Further the same 

quantity will, almost certainly, diminish as the number of electrons 
which come under the influence of the light beam increases : for 
o) fluctuates because all those electrons are not in the same con- 
dition, and in a very large collection of electrons the distribution 
of electrons of different properties is likely to be very nearly the 
same. Accordingly, on the older theory of light, we should expect 

— to be very small : for any light disturbance is spread over the 

whole surface of the cell and of the optical train, and acts upon a 
vast number of electrons. But, on the theories of light which 
form the basis of this experiment, the area of the surface affected 
by any one light disturbance is very small and the number of 
electrons in that surface may possibly be as small as one. With 
these considerations in mind, let us consider how observations of 
the fluctuation of the measuring instrument might be applied to 
test the rival theories. (It must be remembered that, in any 
comparable series of experiments, f{t) will be the same, so that 
Ot^ is proportional to x^jr.) 

In the first place we might compare the fluctuations of X— X', 
i.e. the fluctuations of the balanced cells, (1) when we know that 
the two beams are independent and (2) in the case in which we 
wish to discover if they are independent. The ratio of the 
fluctuations in (1) to those in (2) should be 1 if the beams in 

(2) are independent, and — z= — if they are dependent. If jf 

ff _ 


were the same in both cases and — were large compared to 1, 

the two ratios might well be indistinguishable : it is for this 

reason important to note that —^ is certainly not likely to be 

large on the ' spherical wave ' theory of light. If that theory be 
true we should expect the ratio in case (2) to be much greater 
than that in case (1); if the 'bundle of energy' theory be true 
we should expect the two ratios to be equal. The objection to 
this method of test is that it is difficult to ensure that the optical 
trains and the entire apparatus remain the same, when the change 
is made from the beams known to be independent (probably two 
different lamps) to the beams which it is desired to test. 

In the second place, we may compare the fluctuations of 


316 Mr Camphell, Discontinuities in Light Emission. 

X — X', with those of X or of X', by simply putting one of the 
two beams investigated out of action. If the two beams are 
independent the ratio of the fluctuations in the first case to those 
in the second should be 1, if they are dependent it should be 

2^ . .... . . 

-^=. Here again a distinction will be possible only if rf for 

ft)^ + rf 

the dependent beams is small compared to eo^. The objection 
to this method is that, as will be seen, it is not easy to exclude 
sources of fluctuation which affect the single cell, but do not affect 
the balanced cells. 

% 10. Let us now investigate briefly the quantity f^(t)dt. 

It can be shown by mere algebra that, if the form oif{t) given 
in equation (2) of the previous paper is correct, involving the 
constancy of the capacity of the system and the proportionality 
of/(i) to the charge communicated to the instrument, we have 

r fHt)dt-~ oc^ip + ct + 0) 

O' ' 4ap(p + a' + b') 

according as a and /3 are real or imaginary*. Here e is the 
charge on an electron, C the capacity of the system, R the re- 
sistance between the quadrants of the electrometer, p = l/MG the 
logarithmic constant of decay of the charge, a and /3, or a and b, 
time constants determined by the period and damping of the 
electrometer, and s the sensitiveness of that instrument, i.e. the 
ratio of the deflection to the steady p.d. between the quadrants. 

The following deductions from (11) and (11') are important, if 
it is desired to make d^'^ as large as possible : 

(1) It is desirable to decrease G as far as possible : but, taking 
into account the fact that p is a function of C and (4) below, C 
practically enters only as the first power and not as the square. 

(2) s should be made as large as possible. Since s enters as 
its square its value is far more important than that of G. 

(3) R should be made as large as possible. It will be seen 
that there are practical limits to the value of R. 

(4) So long as p is small compared with a and j3, or a and h, 
which are of the same order of magnitude in all ordinary instru- 

* It should be remarked that the previous paper is deficient in its algebra. It 
■was not noticed that equation (20) can be reduced to the form given here and, con- 
sequently, the conclusions of paragraph 10 as to the most desirable values of the 
instrumental constants are worthless. The conclusions given here are believed to 
be correct, subject to further considerations given below in paragraph 15. 

Mr Campbell, Discontinuities in Light Emission. 317 

ments, the value of a, ^, a, h is of little importance. If a = 6 and 
ajp is changed from infinity to 1, the value of Ot^ is only decreased 
in the ratio 5 to 3. 

This conclusion may be surprising till it is remembered 
that f{t) represents bhe motion of the needle after a sudden 
disturbance. The values of the time constants of the instru- 
ment, supposed smaller than that of the high resistance, affect 
only the initial part of the motion. 

Accordingly it is clear so far that the sensitiveness of the 
instrument is the one thing that really matters. A Dolezalek 
electrometer will be much preferable to any form of electroscope 
with smaller capacity but smaller sensitiveness ; for the capacity 
of the system apart from the electrometer will not be insignificant 
compared with that of the electrometer. 

The actual experimental arrangements will now be described. 
Although no results have been obtained as yet, I think that, in 
all essentials, they have attained a final form. But since no results 
are claimed as yet, a very detailed account will not be necessary. 

In all quantitative statements that follow, electrostatic units 
are employed. 

§ 11, In the earlier experiments the source of light was a 
Nernst lamp of 50 watts heated by the town alternating supply 
which was the most constant source of current available. To 
indicate changes in the intensity of the light a small thermo- 
element in a vacuum was placed immediately under the lamp : 
changes of 1 in 10,000 could be detected with certainty. Since 
the constancy of the light proved insufficient an attempt was 
made to use an Osram lamp of 8 volts and 16 watts, but, though 
by the use of two such lamps some preliminary observations on 
the fluctuations of two independent sources have been made, the 
intensity of the light was insufficient for the main experiment. 
It is hoped in the near future to be able to run a Nernst lamp of 
50 or 100 watts off" accumulators of constant potential. 

When continuous current was used to excite the lamp, its 
constancy was measured by making the filament one arm of a 
Wheatstone bridge, for which the exciting battery served as the 
source of current. A change of 1 in 10^ of the resistance could 
be detected, or, since the illumination appears to vary approxi- 
mately as the 10th power of the resistance, a change of 1 in 10* 
of the illumination. 

The light from the lamp was rendered parallel by a simple 
lens of 7'5 cm. focal length and 4'5 cm. aperture. The resulting 
beam was split into two parts, either by interposing in its path a 
half-silvered mirror, or two full mirrors, one behind the other, of 
which the front mirror had a sharp edge ; the plane of the mirrors 

318 M7' Gamphell, Discontinuities in Light Emission. 

made an angle of approximately 45° with the direction of the light. 
The resulting two beams were suitably reflected by mirrors and 
brought to a focus on the surface of the alloy in the photo-electric 
cells by lenses similar to that previously mentioned. The angle of 
incidence of the light on the surface of the alloy was approxi- 
mately 65°. 

In order to adjust the currents through the two photo-electric 
cells to equality, a shutter moved by a fine screw was inserted in 
front of one of the cells. The light acting on the cells in the 
absence of the shutter was first adjusted as closely as possible to 
give equal currents, and the final adjustment made by means of 

The figure shows only one cell ; the 
second cell was exactly similar and 
lay beneath the plane of the paper. 

the shutter. The primary adjustment was made by varying the 
distance of the lamps from the cells, when two independent lamps 
were used : by moving the front mirror across the path of the 
beam, when the light from a single lamp was split by two full 
mirrors : and by altering the inclination of the half-silvered mirror 
to the path of the light, when the splitting was effected by the 
half-silvered mirror. 

§ 12. As photo-electric cells an attempt was first made to use 

Mr Campbell, Discontinuities in Light Emission. 319 

rubidium cells made by the Polyphos Elek. Ges. of Munich : but, 
though these were more sensitive than any made subsequently, 
the differences between various cells were too great to permit of 
their use. It should be noted that these cells, unlike those made 
usually by the firm, were exhausted to the highest possible 
vacuum. It is necessary in these experiments to avoid the 
presence of any gas in the cells which might give rise to ' ionisa- 
tion by collision,' for two reasons. (1) If there is ionisation by 
collision it is very improbable that the fundamental assumption 
of the theory given above, that the current through the cells is 
simply proportional to the number of light disturbances incident 
upon it, is fulfilled. (2) As was pointed out in the previous 
paper*, if the current is not saturated, the effective value R of 
the resistance between the quadrants of the electrometer varies 
with the intensity of the light : there is a portion of the con- 
ductivity which does not depend on the properties of the conductor 
inserted specially, the magnitude of which it is almost impossible 
to measure, and the constaacy of which cannot be assured. 

Cells were then made containing the alloy of sodium and 
potassium. The form ultimately adopted is shown in fig. If. 
After the vessel had been evacuated the alloy was sucked into 
the bulb A. When the evacuation had been completed it was 
allowed to flow into the vessel 5 by inclining the structure. 

The difficulties which attend the use of the alloy have been 
discussed recently so fully by Elster and GeitelJ that little more 
need be said. Of the two great difficulties which they found, the 
distillation of the alloy on to the other electrode and the con- 
tamination of its surface with particles of oxide, the former was 
of no importance in this work and the latter of but slight 
importance. The presence of oxide would only increase the value 
of rf. But a method was found of getting rid of the small specks 
of oxide by a process much simpler than filtering. If, when the 
alloy is in its final position, one point at its edge is warmed 
slightly (the neighbourhood of the hand is sufficient) the change 
in the surface tension is sufficient to drive all impurities to the 
opposite wall of the cell, leaving a perfectly clean surface. The 
warm body must be kept in position while the experiment is in 
progress, but the most careful experiments failed to show any 
changes in the conductivity of the cells due to its presence. 

The cells were exhausted by charcoal immersed in liquid air 
before being placed in position. A second tube of charcoal was 
always kept in liquid air while observations were in progress. 

* Campbell, loc. cit. § 16. 

+ The tube joining A and B should have been drawn so that it joins B between 
the copper plate and the surface of the alloy. 

+ Elster and Geitel, Pliys. Zeit. x. 1909, p. 457. 


Mr Campbell, Dmontinuities in Light Emission. 

Fig. 2 gives the relation between the potential ditferenee on one 
of the cells and the current through it. It will be seen that very 
complete saturation is attained : the point on the curve which is 
marked by the cross corresponds to the P.D. actually used in the 

The electrodes of the two photo-electric cells Avere connected 
with the battery of small accumulators, which provided the po- 
tential used, in such a way that the currents through them to the 
electrometer were opposite in sign. See fig. 3 which shows the 
connections of the measuring circuit. 









p. D. (E.S.U.) 


Fig. 2. 

§ 13. The electrometer employed was of the Dolezalek pattern. 
The constants a and /3 (real for low potentials on the needle, and 
imaginary for high potentials) were changed by altering the 
potential on the needle. These constants were determined in the 
ordinary way by observing the motion of the needle when dis- 
placed from its zero position with the quadrants kept at constant 
potential. The sensitiveness in most cases was about 10", the 
scale being 1 1 metres distant and capable of readings to |- division. 

A tilted electroscope was also connected to the common 
electrode of the cells. It was more convenient than the electro- 
meter for some purposes, such as the measurement of the total 
current through either cell. It was for such measurements that 
the capacity box (9 x 10- to 9 x 10^) shown in fig. 3 was employed. 

Mr Campbell, Discontinuities in Light Emission. 321 


Fig. 3. 

^1, /^g photo-electric cells. 

Bj small accumulators. 

B^, Bo accumulators for potentiometer circuits Pj, Po 

G sub-divided capacity box (1 micro-farad). 

E electrometer. 

E' tilted electroscope. 

R Xylol-alcohol resistance. 

G, G' guard-rings. 

K key insulating electrode system. 

1^22 J/r Ca))ipbc!L Disconfijiiiltic.'^ in Liaht Eiuis.-^'io)!. 

§ \4f. The rosistnnoo bv which the oloctronuMor was shuntod 
Nvns of the order of j\i K.s. U. (^}) x 10'" ohinsV Sueh resistanees 
;vre too low to be provided bv ionised air in the manner now 
associated with the name of Bronson : niovco\ or, such air re- 
sistances give rise to fluctuations, due to the tinitude of the 
number of rays bv which the air is ionised, which wonUl be of 
the same order of magnitude as those thai are h(Me invest.igatcii 
Several substances were ti'ied as materials tor the required re- 
sistance, inchidino; graphite, copper oxide, Phillips' conducting 
glass and vaivious liquids. The latter e\ entualiy proved the most 
satisfactory. A mixture of Xylol ami b'thyl Alcohol (frou\ JH) 
to 5 parts of the former to 1 of the latter) was ultin\ately em- 
ployed in a tube oi' such a form that the distance between the 
platinum electrodes could be varied. One end o( the resistance 
was connected to the common electrode of the cells, the other to 
a potentiometer arrangement, the need for which will be explained 

The insulation of the electrode system, of sulphur and amber, 
was such that its conductivity was certainly less than O'Ol of that 
of the artificial resistance: its conductivity is therefore neglected. 

The value of R was determined directly by Ohm's Law. One 
of the cells being kept dark, the light falling on the other was 
adjusted to such an intensity as to give a convenient current 
through the cell. The magnitude of this current was measured 
by the electroscope and capacity box — the electrometer being 
taken out of the circuit. The electrometer was then connected 
again and such a potential applied to the potenticMneter /*, that 
the electrometer showed no detlection. Then the potential between 
the ends of the resistance \vas such that the current through the 
resistance was equal to that through the photo-electric cell. In 
this manner it could be shown that the resistances used obeyed 
Ohm's Law with an accurai'v of 1 '7o *-"*^'*^^i' •"'' ^*!>i\i^«^ ^">f I'-i^- ^'"^>'" 
1'5 to 0002 E.s.U. The polarisation E.M.F. of the liquid resistance 
was certainly less than lO""* E.S.U. 

§ 15. The only quantity in equation (11) the measurement of 
which presented any dithculty was the capacity. T'he capacity 
of the electrometer was a considerable part of that of the whole 
electrode system, and it is well known that, this capacity is not 
constant, but varies with the delleciit>n and, so far as l can n\ake 
out, with the rate of movement, oi' the needle. The most hopeful 
way of obtaining an etll'ective value for the capacity of the electroilc 
system appeared to be by measuring the value of 11 and of 
/) = l/BG : p was determined by observing the rate of decay of 
the detlection of the electrometer, when the electrode system was 
raised to a given potential and then insulated. (The initial part 
of the decay was neglected, because of the inlluence of the time 

Mr Campbell, Discontinuities in Light Emission, 323 

constants of the electrometer.) If the capacity of the system 
varies with the deflection, the resulting curve of deflection against 
time ought not to be exponential. As a matter of fact, it ap- 
peared to be perfectly exponential, but, on. the other hand, the 
calculated value of the capacity increases regularly with a decrease 
in R. On decreasing R from 0*13 to 0'013 G appeared to increase 
from 380 to 600. 

That this peculiarity was due to the electrometer was proved 
by the fact that, if the electrometer were disconnected and the 
decay observed by the electroscope, the capacity being varied by 
means of the capacity box, perfectly consistent results were 
obtained. A great deal of time was wasted in an inquiry into 
this matter and no conclusive information was obtained. The 
matter is not of first class importance, because in comparing 
fluctuations, care would, of course, be taken to keep the instru- 
mental constants the same : and, in estimating the absolute value 
of N{(o^ + ri^), the errors in the measurement of the fluctuations 
arc likely to be as serious as the uipicertainty in the value of 
the capacity. 

§ 16. It will be well to consider here for a moment whether 
the magnitude of the fluctuations to be expected on the theory 
of light which is under discussion is such that it is likely to be 
capable of detection and measurement. On Planck's theory some 
estimate of this magnitude can be made. 

According to that theory the quantity of energy (e) contained 
in one light disturbance is given by 

e = 6*5 X 10~^^ V, where v is the frequency of the light. 

Hence if we know the amount of energy in each of the electrons 
shot off from the photo-electric substance, we can deduce the 
average number of electrons shot off by each light disturbance : 
i.e. the quantity to. The application in this manner of Planck's 
theory to the photo-electric effect has been made by Einstein* 
and by Joff^f, the latter giving numerical calculations based upon 
the work of Ladenburgj'. It appears from these calculations that 
the energy given by the light to the electrons shot out from zinc 
is about one-third of that contained in each light disturbance : so 
that Q) is about 3. For the alloy of sodium and potassium, which 
is more photo-electric, co is certainly greater. But, since a mini- 
mum estimate is desired, we will take eo as 1, and will put 
v" = — though, if CO is as small as 1 it is probable that tj'^ is of 
the same order as co. 

* Einstein, Ann. d. Phys. xx. 1906, p. 199. 
t Joff6, Ann. d. Phys. xxiv. 1907, p. 939. 
X Ladenbnrg, Pliys. Zeit. viii. 1907, p. 590. 

324 Mr Campbell, Discontinuities in Light Emission. 

The total current through either cell {i) is given by 

i = eQyN (12). 

The magnitudes of the various measured instrumental constants 
in the experiments which have been made are approximately as 
follows : 

(These values are not the most favourable that can be obtained 
experimentally, so that our estimate is once more a minimum 

a = 6 = 0-2, R = 0% (7=500, s = 10«, ^ = 100. 


Assuming that the value of | f^ {t) dt can be calculated from 

(11'), it is found to be about 2 x 10^ el Hence for the fluctuations 
of the balanced cells illuminated by independent sources 

0^ = 2 {(o' + ^) N .2 .lO'e^ 

= 4 . 10^ . €1 


_ = 16, 

or Je^^ = 4 (about). 

This value is just on the limit of the range within which 
detection is possible — it means that the electrometer spot will be 
on the average about 4 divisions distant from its mean position. 
But this is a minimum estimate : as a matter of fact such pre- 
liminary observations as have been made with two independent 
sources (two Osram lamps) indicate that, with these values for 

the instrumental constants, Jd^'^ is about 18 — which is of the 
right order of magnitude. 

§ 17. A brief explanation must be given of the manner in 
which the observations were taken and the value of 6t^ deduced 
from them. 

This quantity is the arithmetic mean of the squares of the 
deviation of the indicator from its mean position for all times 
after a period T from the moment that the electrode is insulated. 
As was pointed out in the previous paper, the most satisfactory 
way of estimating djf'^ would be by recording the motion of the 
spot photographically and integrating the resulting curve (with 
the ordinates squared) graphically. But since, at least at 
present, no great accuracy has been required, the observations 
have been taken by eye at equidistant intervals of time (4") 
indicated by a metronome. 200 such observations constitute one 
series, of which the probable error is, as has been shown, 1/V200. 

Mr Campbell, Discontinuities in Light Emission. 325 

In almost all series there was, in addition to the fluctuations, 
a slow drift of the spot in one direction or the other. To allow 
for this drift, it was assumed to be linear so that 

ei=u + vt (13). 

It is easy to see that, if we treat the n observations made as 
readings from which the constants u and v are to be determined 
by a least square solution, 6t'^ is the mean of the square of the 
residuals, so that 

W' = te^ - (?^ _ -^4%; i^ 2^, - s (< . ^4'-(i4). 

n n{n^— 1) ( 2 J 

Any series in which there appeared to be any suspicion of a 
change in the drift was rejected. 

The arithmetical work in finding 0^'^ Avas heavy, but with 
practice and the aid of a calculating machine a single series could 
be solved in 20 minutes. 

§ 18. At the beginning of the work a great deal of time was 
wasted because a complete theory of the experiment was not 
known. But once the influence of the various instrumental con- 
stants upon the fluctuations was discovered, all the experimental 
difficulties which had been anticipated were quickly overcome. 
They were such as attend all work upon electrostatic currents and 
no further reference need be made to them. 

Blank experiments, made without the action of the light at 
all, showed that, when no light acted, there were no fluctuations 
whatever. For two hours or more the spot on the scale would 
keep perfectly steady or move constantly with a very slow drift in 
one direction. It is certain, therefore, that no trouble need be 
expected from such sources as changes in the potential of the 
battery used to send the current through the cells. 

It was also important to show that the high resistance did not 
introduce disturbing fluctuations, such as would certainly have 
been introduced by a Bronson air resistance. For this purpose 
two similar high resistances were used and opposite potentials 
applied to their ends, so that the currents flowing through them 
were opposite in direction and equal in magnitude to each other 
and to the photo-electric current employed. No fluctuations what- 
ever could be detected, though the steady drift of the spot was 
greater than in the former case, when practically no current was 
flowing through the resistance. 

§ 19. But there were two outstanding difficulties. The first 
of these, the difficulty of determining the capacity, has been noted 
already. The second was far more serious and has prevented, up 

326 Mr Campbell, Discontinuities in Light Emission. 

to the present time, any results being obtained. It Avas found 
that the balance of the two currents through the cells was upset, 
if the total intensity of the light was changed. Whether the two 
currents were excited by different lamps lit by the same current 
or by the light from a single lamp split into two parts, a change 
in the current supplying the lamp or lamps was attended by a 
very serious displacement of the balance of the currents. 

A great deal of work has been done in the effort to discover 
the cause of this defect and to remove it : but it has remained as 
mysterious as ever. It was thought at first that the cause must 
lie in some asjmimetry of the photo-electric cells*. 

That this explanation is not sufficient was shown by focussing 
the two beams, not on photo-electric cells, but on thermo-elements. 
Though these elements were much less sensitive than the cells, 
there was no doubt that the balance of the thermo-elements was 
upset in exactly the same way as the balance of the photo-electric 
cells by a change in the total illumination. It appears then that 
the effect is connected rather with the optical train employed than 
with the detectors : and additional evidence for this view was 
found in the fact that the sign of the change in the balance could 
be changed by comparatively trifling alterations in the mirrors 
and lenses. But in no case were attempts to reduce the change 
to zero successful. 

The magnitude of the change in balance (measured relatively 
to the whole current passing through either cell) increases very 
rapidly with an increase in the total light. By placing diaphragms 
before the lamp and causing a given increase in the illumination 
by shunting a constant resistance in the lamp circuit, it was found 
that the change in the balance varied approximately as the cube 
of the total light. 

It Mas thought at one time that the change in the balance 
might be due to the fact that there was a portion of the current 
passing to the electrode which was independent of the light. It 
is easy to see that, if there were such a portion, the balance 
between the currents would hold only for one intensity of the 
light. The experiments that have just been noted show that 

* It was thought at one time that the reason might lie in the fact that the 
em-rent through the cells was not strictly proportional to the intensity of the light 
acting upon them : and observations were made with the object of testing this 
proportionality. The variations in the intensity of the light were produced by 
passing it through a photographic lens in which diaphragms of known aperture 
could be inserted. It was found that the current was not proportional to the light, 
being relatively smaller for smaller intensities of the light. It was discovei-ed sub- 
sequently that a similar result for ultra-violet light acting on zinc had previously 
been noted by Griffith {Phil. Map. vi. 14, 1907, p. 297). But the matter is not 
very important for our purpose, because all that is necessary, in order that a 
change in the total light should not alter the balance, is that the current should 
be the same function of the lia-ht in the two cells. 

Mr CciAnphell, Discontinuities in Light Emission. 327 

such a cause cannot account for the whole of the effect : but it was 
found that by introducing a current independent of the light the 
magnitude of the effect could be decreased very considerably. 
Such a current was introduced by raising the end of the high 
resistance R distant from the electrode to a suitable potential, 
instead of connecting it to earth and the earthed quadrants of 
the electrometer. The magnitude of this potential had to be 
found by trial. But though the effect could be reduced greatly 
by this device, it could not be entirely abolished. The best state 
of affairs that could be produced was when, on changing the total 
light, the spot on the scale first moved rapidly a short distance in 
one direction and then gradually took up a final position on the 
other side of the zero corresponding to the new balance. 

§ 20. The change of balance was of especial importance in the 
earlier experiments, because the most constant source of potential 
which was available for a Nernst lamp was subject to variations of 
as much as 5 °/^. But at the outset it was not even thought 
worth while to make special efforts to obtain a more constant 
source, until all possible investigations into the matter had been 
made. If there were any uncertainty whether the observed 
fluctuations were due to changes in the total intensity of the 
light or to changes in the relative intensity of the two beams, 
the experiments could be of no possible value. It was only when 
all efforts to get rid of the difficulty had failed that it seemed 
desirable to proceed further. 

It appeared, then, that errors due to this source could be 
detected, if not eliminated, by comparing the fluctuations due to 
one of the cells with those due to both of the cells illuminated by 
totally independent sources. Changes in the total intensity of 
the light, even if they affect the latter experiment, must be much 
more serious in the former. And, if it were found that these 
changes were so small that the fluctuations in the former case 
were, as theory indicates, half those in tlie latter, then it would 
be certain that the fluctuations were due to changes in the 
relative intensity of the two sources and not to changes in the 
total intensity of the light. 

In order to measure the fluctuations due to one source 
separately, the current through the photo-electric cell was 
balanced by Meyer and Regener's method of sending an equal 
and opposite current through the high resistance R by applying 
to its ends a P.D. by means of the potentiometer. It is not in- 
tended in this paper to give any actual results, but it has been 
found that the total light from two Osram lamps run from the 
same battery in parallel is so constant that the theoretical relation 
is fulfilled within the limits of error: the fluctuations of one 

328 Mr Campbell, Discontinuities in Light Einission. 

source are certainly less than those of two : and, accordingly, the 
main source of the fluctuations must lie in changes in the relative 
intensities of the lamps. 

It is for this reason that the work that has been done appears 
of sufficient promise to justify publication. If results are ulti- 
mately obtained, the description of the methods and the narration 
of the results would be so lengthy that it appears desirable to 
divide thus the account into two parts. 

Mr Horton, The emission of positive rays, etc. 329 

The emission of positive ray s from heated phosphorus com^pounds. 
By Frank Horton, M.A., St John's College. 

[Bead 25 October 1909.] 

Prof. Sir J. J. Thomson has shown that certain salts when 
heated give- rise to a large positive ionisation*. Of the salts he 
experimented with the greatest effect was given by phosphates, 
and of these aluminium phosphate was found to be the most 
active. From this salt at a red heat Sir J. J. Thomson found 
that the emission was so great as to be easily measured with a 
galvanometer. The following experiments were made with the 
object of discovering whether there was any connection between 
this phenomenon and the "anode rays" of Gehrcke and Reichen- 
heim. These experimenters have found -f* that when certain salts 
are used as anodes in a vacuum tube they give off positive rays 
which proceed at right angles to the surface of the anode and 
behave in a manner completely analogous to that of cathode rays. 


A, anode. K, cathode. 

These anode rays consist of positively charged particles of atomic 
dimensions moving with a velocity of about 10'' cms. per sec. 
Spectroscopic evidence has proved them to consist of atoms of 
the metal contained in the salt anode. Gehrcke and Reichenheim 
found that anode rays were most freely emitted by the halogen 
salts of the alkali metals, and they consider that in general the 
most suitable salts to use as anodes are those which are easily 
fusible and easily dissociated by heat. The halogen salts experi- 
mented on by Sir J. J. Thomson were found to give a small excess 
of positive electrification when heated, but nothing nearly so great 
as that given by the phosphates. 

Aluminium phosphate was the salt first used in the present 
experiments, and tubes containing this were employed as anodes 
in an apparatus (see Fig. 1) similar to that described by Gehrcke 

* J. J. Thomson, Proc. Camb, Phil. Soc. Vol. xiv. p. 105. 

t Gehrcke and Reichenheim, Ann, der Phys. xxv. p. 861, 1908. 

VOL. XV. PT. IV. 22 

380 Mr Horton, The emission of positive rays 

and Reicheiibeim. The discharge tube was a round-bottomed 
flask of some oOO — 1000 c.c. capacity. It was connected to a 
mercury pump and McLeod gauge, and had a charcoal tube 
attached for producing a low vacuum by means of liquid air. 
Owing to the high melting points of the salts used in these 
experiments, the tube A, which contained the anode, was of 
fused quartz, 2 mm. internal and o mm. external diameter. The 
aluminium phosphate to be used as anode was tinely powdered 
and mixed with a little powdered graphite to render it conduct- 
ing, and also with a little silver chloride to bind the mass together 
when heated. This mixture was rammed into the end A of the 
quartz tube to a length of 2 — 3 cms. The tube was then strongly 
heated in a blow-pipe flame. This caused the silver chloride to 
melt, and on cooling the mixture was tirmly held in the tube. 
Electrical connection with this mixture was made by means of a 
copper wire introduced into the tube at the other end and pushed 
into the mixture while that was still hot. The cathode is the 
aluminium ring K at the end of an aluminium wire, the straight 
part of which is covered by a glass tube as shown in the diagram. 
These tubes, from the anode and cathode, pass through holes in an 
ebonite bung which closes the mouth of the flask, the joints being- 
made aii'-ticrht with sealing-wax. 

The discharge through the tube was sent from a large Marconi 
induction coil. It would have been better to have used a large 
Wimshurst machine (following the method of Gehrcke and Reichen- 
heim), but there was not one available. A spark-gap and a valve 
of Lodge's pattern were usually placed in the secondary circuit of 
the coil in order to prevent, as far as possible, the current from 
passing in both directions. 

Perhaps it may be of interest to mention here that for obtain- 
ing quickly the low vacuum required in these experiments, it was 
found to be of great advantage to have the tube containing the 
charcoal for cooling in liquid air made of fused quartz. During 
the preliminar}' pumping a blow-pipe flame was played directly on 
to the quartz tube, and in this way the charcoal was more quickly 
and more completely freed from occluded gas. 

When the induction coil discharge passed through this tube 
(the gas pressure being so low that no luminous gas was seen in 
the bulb) the " torch " of light at the anode, described by Gehrcke 
and Reichenheim, was obtained. On examination, the spectrum 
of this light was found to contain the brightest silver lines, but no 
lines of aluminium could be detected. In a magnetic fleld part 
of the luminosity was deflected in the direction which would mean 
that the rays consisted of positively charged particles leaving the 
anode, and partly in the opposite direction, but I could never be 
quite sure that this was not due to the discharge from the coil 

from heoied phosphorus compounds. 331 

passing in both directions. The light at the anode never showed 
the fine bright pencils so characteristic of the anode rays, and 
the spectrum proved that if any anode rays were produced they 
were due to the silver chloride, and not to the aluminium 

Other methods of making the aluminium phosphate into a 
solid mass, capable of being used as an anode, without mixing 
with an}' substance likely to produce anode rays, were tried, but 
without success. It was therefore decided to use some more 
fusible phosphate, and a mixture of sodium and lithium pyro- 
phosphates with a little graphite was heated in the quartz tube 
until it fu.sed. This tube was then fitted up as the anode in a 
bulb similar to that described above. On evacuating and passing 
a discharge this tube behaved in a curious way. When the 
pressure was not too low, there was a torch of light surrounding 
the anode, in front of this a dark space, and then at about the 
centre of the bulb a little ball of luminosity, which probably 
corresponded to a striation in the pjositive column. On putting 
on a magnetic field transverse to the direction of the rays from 
the anode, the torch seemed to jump out nearer to the glowing 
ball, at the same time spreading out symmetrically about the axis 
of the anode, and curling round towards the cathode ring. The 
appearance was as though a stream of rays were suddenly brought 
up against a barrier. The effect produced seemed to be inde- 
pendent of the direction of the magnetic field, so long as the lines 
were at right angles to the direction of the discharge. That 
sodium was shot off' from the anode could be seen by the gradual 
appearance of the yellow sodium light upon the cathode — appear- 
ing at first on the side nearer to the anode and gradually spreading 
all over it. The spectrum of the light at the anode showed the 
lines of sodium and lithium brilliantly, also the brightest mercury 
lines, including the tliree new lines in the orange the wave- 
lengths of which are given by the author in a previous paper* 
as 6232, 6121, 6070. 

In a more perfect vacuum the gas luminosity in the bulb 
disappeared, but the glow at the anode remained. There was 
however no sign of the fine pencils of light, with the accompany- 
ing phosphorescence of the bulb, which is so characteristic of the 
anode rays. In a magnetic field the glow at the anode was mostly 
deflected in the positive direction, but there was some which 
behaved as though it were negatively charged. In order to decide 
whether the rays deflected in the positive direction were really 
positively charged, or whether they were negatively charged rays 
travelling towards the anode, their behaviour in an electrostatic 

* Proc. Camb. Fhil. Hoc. Vol. xiv. Pt 5. 



Mr Horton, The emission of positive rays 

field was investigated. For this purpose the apparatus dia- 
grammatically represented in Fig. 2 was used. The rays leaving 
A were made to shoot through the hole in the earth-connected 
screen S, and then between the parallel plates Pj, P^, which were 
about 3 cms. long and placed about 1 cm. apart. A strong electric 
field could be created between these by connecting them to the ter- 
minals of a battery of small accumulator cells. Z is a zinc-blende 
screen by means of the phosphorescence of which the deflection 
of the rays could be observed even when the illumination along 
their path was very faint. 

s A 

Fig. 2. 

A, anode. S, earth-connected screen. Z, zinc-blende screen. 

C, cathode. Pj, P2, parallel aluminium plates. 

As with the former apparatus it was found that there was no 
fine pencil of rays given off by the anode. The rays getting 
through the hole in the screen S were always deflected towards 
the positive plate by the electric field, showing that they were 
negatively charged. They were, no doubt, ordinary cathode rays 
formed by the reversals of the induction coil. The impossibility 
of obtaining anode rays from these phosphates seems to show that 
there is no connection between the anode rays and the positive 
electrification emitted by salts when heated, but it was thought 
worth while seeing whether anode rays could be obtained from 
other compounds of phosphorus, because these, as well as phosphorus 
itself, have the power of emitting positive ions when heated on 
the anode of a vacuum tube. 

Some experiments were therefore made in which calcium 
phosphide mixed with a little graphite was used as the anode 
in the apparatus of Fig. 1. At a low pressure a distinct torch 
of rays was seen surrounding the anode, and, after a few minutes, 
from the midst of this torch there came a fine pencil of rays 
shooting right across the bulb and causing phosphorescence of the 
glass where they struck. This pencil seemed to have its origin 
at a spot on the surface of the anode which was hotter than the 
rest of the surface. It was not deflected in a weak magnetic field, 

from heated phosphorus compounds. 333 

but was deflected in the positive direction in strong fields. These 
rays were evidently anode rays similar to those obtained by 
Gehrcke and Reichenheim. The spectrum showed some calcium 
lines and other lines which could not be identified in the short 
time during which the rays persisted. Thus we see that anode 
rays can be obtained from calcium phosphide, although they could 
not be produced from the phosphates experimented with. 

Gehrcke and Reichenheim have connected the production of 
anode rays from the halogen salts of the alkalis and alkaline 
earths with their easy fusibility and their property of dissociating 
when strongly heated. The heated salt is supposed to be decom- 
posed electrolytically by the passage of the current, the metal 
being liberated at the surface of the anode and travelling across 
the tube. Close to the anode the electric force is very strong on 
account of the anode fall of potential, and it is in traversing this 
region that the liberated metal atoms obtain their great velocity. 
Some time ago it was shown by Matthies* that the anode fall in 
a vacuum tube was greatly increased by the presence of a halogen 
vapour. In a recent paper Reichenheim -f states that, at low pressures 
and with large currents, the anode fall in the halogens amounts 
to several thousand volts. This abnormally high value Reichen- 
heim thinks maybe explained on the supposition that the halogen 
vapours possess, in a higher degree than other gases, the power of 
absorbing negative electrons. If this be correct, other electro-nega- 
tive vapours should behave in a similar manner, and Reichenheim 
shows that a large anode fall is also obtained in phosphorus 
vapour. In the experiments described in this paper it is probable 
that phosphorus vapour was present in the case of the calcium 
phosphide anode, owing to its decomposition when heated. There 
would thus be a large anode fall and a strong force near the anode 
which would give to the liberated atoms the energy to make them 
luminous anode rays. The phosphates, on the other hand, are 
extremely stable bodies, and in their case there would be no 
phosphorus vapour to cause an abnormal anode fall and con- 
sequently no anode rays. Thus these experiments seem to confirm 
the view of Gehrcke and Reichenheim as to the origin of anode 
rays, and to show that there is no connection between this pheno- 
menon and the emission of positive electrification from heated 

The author wishes to acknowledge his indebtedness to the 
Government Grant Committee of the Royal Society for the means 
of purchasing some of the apparatus used in these experiments. 

* Matthies, Ann. der Phys. xviii. p. 473, 1905. 

t Reichenheim, Verh. d. D. Phys. Ges. p. 168, 1909. 

334 Mr 

Orange, On the shape of beams of canal-rays. 

On the shape of beams of canal-rays. By J. A. Orange, B.A., 
Senior Scholar of Trinity College. (Communicated by Professor 
Sir J. J. Thomson.) 

{Read 8 November 1909.] 

In a recent paper* the writer stated certain conclusions with 
respect to beams of canal-rays obtained in connection with 
" sandwich-kathodes." It was maintained that the canal-ra^/s 
are straight, the curvature of the boundaries of the beam being 
explained by supposing that they are merely the envelopes of 
such rays. 

This point has been tested since by using a mica obstacle and 
observing the form of the shadow in the beam. The method 
of placing the obstacle will be evident from Fig. 1, where m is 
the mica slip, which is attached to the aluminium kathode-plates 
by means of water-glass. The beams of canal-rays were photo- - 

Fig. 1. 

graphed as described in the former paper. The sharpness of the 
boundaries of the beams in the case of hydrogen was remarkable, 
and a considerable degree of sharpness was obtained in the photo- 
graphs, the softening that did occur being attributable to slight 
changes in the form of the beams (due to changes of pressure) 
while an exposure was being made. [The time of exposure was of 
the order of 45 minutes.] Figs. 2 to 6 are copied from photographs 
and illustrate the point at issue. 

The outlines of the beams and of the Crookes' dark space 
at a fairly high pressure are shown in Fig. 2. For clearness' 
sake, the shadows in the beams due to the three pins are omitted. 
The beams will be referred to by the letters shown in Fig. 2. The 
shadows due to the pins in Figs. 3 to 6 are in accordance with the 
explanation adopted. 

With regard to the effect of the mica slip, it may be as well 
to say at the outset that the use of this is liable to serious 
objections. If the mica slip were an obstacle only to the canal- 
rays, the method would be much sounder; but since the mica 
is a local obstacle to the discharge in general, its introduction 

* J. A. Orange, Proc. Camb. Phil. Soc. Vol. xv. Pt. 3, 1909, p. 217. 

Mr Orange, On the shape of beams of canal-rays. 335 

Fig. 2. 

Fig. 3. 

Fig. 4. 

Fig. 5. 

Fig. 6. 

Fig. 7. 

336 Mr Orange, On the shape of beams of canal-rays. 

may produce great changes in the electrostatic field, which is 
known to depend largely on the distribution of ions in the kathode 

Consider the effect of the slip in Fig. 3 in the light of this 
reservation. Beam A, which we hold to originate in the lower 
part of the region, (kathode-rays from the longest side of the 
triangle being the primary agent), contains a sharp shadow as 
shown. Here we can claim that the mica does not interfere at all 
with the discharge from the longest side of the triangle, and hence 
the beam A is formed normally, -the mica simply blocking out 
part of the canal-rays when they have passed through the kathodic 

But now consider the effect on beam B. Here we have to 
deal with canal-rays produced in the N.E. corner of the region, 
the kathode-rays from the medium side of the triangle being 
responsible. The slip, however, is placed so as to interfere con- 
siderably with the discharge (including the kathode-rays) from 
this side. Thus instead of getting a neat shadow in the beam, we 
get an ill-defined dai-k core which is vaguely indicated in Fig. 3 by 
a dotted line of elliptical form. 

The details of Fig. 3 are typical of the appearances for various 
positions of the slip, as may be readily imagined. The effect 
of placing the slip in a more exceptional position is shown in 
Figs. 4, 5 and 6, which correspond respectively to decreasing 

The general tendency is best shown at the lowest pressures, 
e.g. in Fig. 6. The beams are roughly of the forms which would 
be obtained if the right-hand corner of the kathode were 
removed altogether, as indicated by the dotted line in Fig. 7. 

This right-hand corner is certainly fenced off by the mica and 
the pin so that it is prevented from acting as a double kathode ; 
the forms of the beams would seem to be in accordance with this 
fact. The only other feature of interest is the fine pencil of canal- 
rays coming from the aperture between the mica and the pin, and 
visible in Figs. 4 and 5. 

These observations would seem to support the view that 
the constituent csmal-rays are straight. 

I wish to thank Prof. Sir J. J. Thomson for his kindly interest 
in these experiments. 

Mr Wellisch, An Elective Detector, etc. 337 

An Electric Detector for Electromagnetic Waves. By E. M. 
Wellisch, B.A., Emmanuel College. (Communicated by Professor 
Sir J. J. Thomson.) 

[Heceived 6 November 1909.] 

A series of experiments in connection with ionisation produced 
b}^ collision was undertaken by the writer in order to test certain 
theories which he had previously advanced with regard to the 
passage of electricity through gases. The preliminary experiments 
were made with an ionisation chamber containing two parallel 
plane electrodes made of aluminium, and at a distance from one 
another of 2 cm. ; one of these electrodes was connected to a 
source of potential, the other to a Dolezalek electrometer. During 
the course of these experiments it was observed that, when the 
gaseous pressure and the electric field were so chosen that the gas 
was on the verge of breaking down, a very feeble discharge of a 
Rontgen ray bulb placed in the neighbourhood was sufficient to 
produce an exceedingly large deflection of the electrometer needle 
which had previously been stationary; the direction of the de- 
flection indicated the passage of a transient electric current 
through the gas. Further investigation of this electric charge 
produced within the gas showed, however, that the determining 
cause of the deflection lay not in the rays issuing from the Rdntgen 
bulb, but in the electric oscillations set up by electric waves 
proceeding from the induction coil which worked the bulb. The 
Rontgen bulb was henceforth removed and a series of experiments 
was conducted in order to ascertain what degree of sensitiveness 
to electric waves could be obtained from similar arrangements. 
Several forms of ionisation chambers were used, and each of them 
proved sensitive as detectors of extraneous electric waves. The 
accompanying diagram represents the scheme of connections 
employed in one of the trials. In this case the detector consisted 
of a glass tube T (about 4 cm. in diameter) ; the electrodes were 
two plane parallel aluminium discs (each 2 cm. in diameter) at a 
distance apart of 1 cm. The tube was connected to a Topler 
mercury pump and a MacLeod gauge so that the pressure of the 
gas (dry air) could be adjusted and measured. In the diagram B 
represents the battery, one of whose poles is earthed, E the electro- 
meter, R a high resistance (consisting of conducting glass) shunted 
across the electrometer, G a variable capacity, and L a variable 

The sensitiveness of the detector depends naturally on a large 
variety of circumstances ; in fact, in the preliminary trials, it was 


Mr Wellisch, An Electric Detector 

found impossible to record the conditions present when a high 
degree of sensitiveness had been obtained, so that it was a matter 
of difficulty to reproduce these conditions ad libitum. However, 
as a rough example of one set of conditions, it was found that with 
the air at a pressure of '76 mm., and with one electrode connected 
to the negative pole of a battery of 400 volts, the tube would 
respond to faint electric impulses provided the capacity, resistance, 
and self-induction were suitably adjusted ; the electrometer needle, 
otherwise stationary, would be deflected on the arrival of the wave. 
The object of the high resistance R was to cause the needle to 
return quickly to its zero so that any succeeding impulse might be 
readily detected. 












The effect of an extraneous electric impulse is probably to set 
up electric oscillations in the circuit including the vacuum tube ; 
the electric force in these oscillations, when superposed on the 
electric field in the tube, may then suffice to produce a discharge 
in the gas. It is important to notice that this discharge need not 
be, and in most of the cases investigated was not, luminous ; its 
occurrence is manifested merely by the galvanometer or electro- 
meter deflection. In this respect the present detector differs from 
Zehnder's Trigger Tube* in which the induced electric oscillations 
precipitate an electric discharge from an auxiliary battery and thus 
produce a glow in the tube. Another method for detecting electric 
waves which depends upon the same principle is that due to 
Boltzmann '\, In this method a battery is on the verge of charging 

* Wied. Ann. Vol. xlvii. 1892, p. 77. 
t Wied. Ann. Vol. xl. 1890, p. 399. 

for Electromagnetic Waves. 339 

an electroscope through a very small air-gap ; electric waves in the 
vicinity will be detected by the electroscope if they are able to 
excite oscillations of strength sufficient to break down the spark 
gap. In the Fleming Oscillation Valve induced electric oscillations 
are detected by their ability to impart unilateral conductivity to 
the space between a cold cylinder and a hot carbon filament, the 
conductivity being due to the negatively charged corpuscles 
emitted from the heated carbon under the action of a directional 
electric force in the oscillations. 

Comparative tests have been roughly made with the electric 
detector and an iron filings coherer, and have proved quite 
favourable to the former ; a short period electrometer (e.g. the 
string electrometer described by Laby in Proc. Camh. Phil. Soc, 
vol. XV.) seems especially suited for use in connection with the 
present form of detector. 

It was observed also that in ionisation chambers such as those 
described, distinct deflections would occur under certain conditions 
of pressure and voltage in the absence of any electric waves pro- 
duced by the induction coil ; as an example of one set of conditions 
it was found that with the air at a pressure of '76 mm., and with 
one electrode connected to the negative pole of a battery of 480 
volts, frequent deflections occurred. The frequency of these deflec- 
tions varied considerably with the inductance in the circuit ; in 
fact, a small variation of the inductance changed the frequency 
from about 100 to 12 deflections per minute. It is reasonable to 
suppose that these deflections are due also to electric oscillations set 
up in the circuit including the detector. The writer is making 
further experiments with regard to these oscillations, especially 
with the object of determining their origin. 

340 Mr Fryer, Aldabra and neighhouring Islands. 

Aldabra and neighhouring Islands. By J. C. F. Fryer, B.A., 
Gonville and Caius College. 

[Read 22 November 1909.] 
Plate XII. 



The group of islands comprising Aldabra, Assumption, Cosmo- 
ledo and Astove is situated some 270 miles to the N.W. of 
Madagascar and thus lies in the extreme S.W. corner of the 
Indian Ocean. Aldabra has long been known as the last spot 
in the old world on which indigenous giant land tortoises continue 
to exist. It was also known to have a peculiar land avifauna; 
and these facts combined with the discovery of unusual percentages 
of iron, alumina and silica in guano from the locality pointed 
to a possible land connection with Madagascar in previous 

In 1905 the Sealark expedition carried on investigations in 
the Indian Ocean relating partly to the former land connection 
between India and Africa and partly to the formation of the coral 
islands of this ocean. The Aldabra group however was not 
visited and therefore from both points of view a further expedition 
was desirable. Certain of the more general results of this latter 
expedition are set forth in this paper. 


Aldabra is an atoll 24 miles long and from 4 — 10 miles broad. 
The land-rim is very perfect and is divided by narrow passes into 
four large islands called respectively Picard, Polymnie, Malabar, 
and Main or South islands. Round the outside of the atoll is 
a narrow fringing reef which is divided by channels from the 
passes and is indefinite or non-existent on the extreme east. 

To landward the fringing reef is bounded by rocky cliffs 
10 — 20 ft. in height which are overhanging and show evident 
signs of wave erosion. 

The highest point on the land-rim (20 ft. above sea-level) 
is always situated near the sea-cliffs and there is a gradual slope 
to the lagoon which is fringed with dense mangrove swamps. 
Small overhanging cliffs are usually found at high tide mark 
in the swamp and give striking evidence as to the rapidity of 
lagoon erosion. The lagoon itself is very shallow except near the 
passes ; it is muddy towards the outsides and sandy in the centre. 
Small islands and rocks are numerous round its outskirts and all 
show much loss due to erosion. 

The general topography of the larger islands is as follows : 

Mr Fryer, Aldahra and neighbouring Islands. 341 

Picard is noted as possessing on its westward shore a narrow 
stretch of sand on which is built the settlement and which also 
constitutes the only arable soil on the atoll. In the centre of the 
island is a rocky plain with a flat pavement-like surface : it is 
known as Plain Cabris and is the locality from which were 
obtained certain peculiar rocks to be referred to later. The rest 
of Picard is more typical of the atoll as a whole ; the surface of 
the ground has been broken up by rain-water denudation into 
points, pinnacles and sharp ridges, and the whole is covered with 
a dense scrub of Pemphis acidula. This combination of rock and 
jungle, known as ' champignon ' country, forms the great bar to 
exploration in Aldabra. 

Polymnie, Malabar, and the north of Main island consists of 
this champignon country. In the S.E. of Main island however 
another plain of flat pavement-like rock exists. It is covered 
by a somewhat open and varied jungle, and within its boundaries 
are found the only fresh-water springs on the atoll. These are 
situated at Takamaka and consist of pits in the rock about 
5 ft. deep. Sand dunes 60 ft. high occur along the south of Main 
island and have been formed by the action of the prevalent winds 
(S.E. Trades) which blow up sand from the reef and pile it in 
mounds on the shore. The west of Main island is again entirely 
of the champignon type of country. 

Leaving now the general topography of the atoll a more 
detailed account of its structure may be given, and this will be 
dealt with under three heads, (a) structure of land, (6) structure of 
fringing reef, (c) structure of lagoon. 

(a) The land is entirely rocky and the main rock component 
is in all cases coral though complications have been introduced by 
the presence of a quantity of calcium phosphate derived from 
guano. The rock of the land-rim may be divided into three 
classes. The first forms a zone round the outside of the laud- 
rim and is marked by the fact that its component corals are 
very perfect and are almost all in position of growth. This point 
is most important as it proves that the atoll is an elevated reef 
and that it has not been formed by wave piling on a subsiding 
base. The second class is the pavement-like rock before referred 
to : it is composed of broken and often triturated coral with such 
debris as mollusc shells and echinoderm spines, and gives evidence 
that the inner portions of the reef before elevation were either 
dead or but feebly growing. The last class of rock is the 
' champignon ' ; it is a highly metamorphosed coral rock with 
scattered inclusions of calcium phosphate derived from guano. 
Metamorphosed coral limestones from all the islands in this region 
contain inclusions of calcium phosphate, and it is necessary to 

S42 Mr Fryer, Aldahra and neighbouring Islands. 

credit the latter substance with some power of inducing meta- 
morphosis though its nature is not understood. In all the three 
classes of rock pits and subterranean caverns are numerous and 
usually contain salt-water which fluctuates tidally. They all 
show signs of erosion and are increasing in size. Evidence is thus 
given that the reef as a whole before elevation was but badly 
consolidated and that even now water can percolate completely 
through the land-rim. 

A few exceptional rocks remain to be dealt with. He Esprit, 
in the lagoon, consists of a ridge of rock half a mile long and 
some 30 ft. high, and is thus the highest rocky point on the atoll. 
The body of the ridge consists largely of calcium phosphate : 
on its sides are pinnacles and walls of a much denuded rock 
composed almost entirely of mollusc shells. Plain Cabris on 
Picard island again shows somewhat similar structures but a 
crystalline mineral resembling apatite should be noted as also 
fossil bones of the giant land tortoise. It may be mentioned 
that Esprit island is of special importance if an attempt is 
made to reconstruct the early stages of Aldabra after elevation. 

(6) The second section of the atoll consists of the Fringing 
Reef. Evidence obtained from the amount of wave erosion and 
from rocks of elevated coral limestone still in situ proves that the 
fringing reef of Aldabra is a ledge of elevated coral rock cut down 
to low water mark and preserved at that point by growing 
lithothamnia and by the piling of sand and coral on the fiat. 
The fringing reef of Aldabra therefore is not a sign of the 
increase of the atoll seaward, but on the contrary is evidence 
of the loss of land owing to wave erosion. 

(c) The last section of the atoll is the lagoon, some of the 
features of which have already been mentioned. Those to be 
further treated are the extent of lagoon erosion and the formation 
of passes. Judging by the maze of small islands and rocks, once 
part of the land-rim, at least two-thirds of the lagoon were at one 
time land. It is still increasing for the rock is reduced to mud ; 
the mud is swept to sea and the land continues to diminish. 
Contrasting lagoon erosion with sea erosion it will be noticed 
that while the latter is uniform over any stretch of coast the 
former is just the reverse, and is extremely irregular. Passes 
therefore must be formed from the lagoon side of the land-rim 
and not from the sea. All stages of pass formation are shown 
on Aldabra. At Camp Frigate the mangrove swamp passes 
completely through the land-rim to the sea, though but little 
water flows through yet. The western channels show complete 
passes through the land-rim but the fringing reef has not yet 
been divided. Grande Passe finally is a pass with a complete 
channel, and it further shows that the channels of the passes 

Mr Fryer, Aldahra and neighbouring Islands. 348 

do not increase indefinitely in size though the land continues 
to be cut down as far as low water mark. This point will be 
further illustrated by the atoll of Cosmoledo, which will be 
described later. The structure of Aldabra has now been described, 
and before proceeding further it may be mentioned that any 
land connection with Madagascar is shown to be obviously 

The Flora and Fauna of Aldabra must be treated very briefly 
for the collections are not completely worked out. 


The Flora contains, oecologically, the following sections : 
(1) Pemphis jungle which grows on metamorphosed rock and 
contains little but Pemphis acidula. (2) Open country jungle 
which contains a varied vegetation of Madagascar origin. (3) Man- 
grove swamp containing three genera of Rhizophoraceae and 
also the pseudo-mangroves Avicennia, Sonneratia and Carappa. 
(4) Shore zone containing typical coral-sand plants such as 
Tournefortia argentea and Scaevola koenigii. The zone owes 
its origin to the fact that sand is blown on to the land from the 
reef and forms a little soil near the shore. 


The Mammalia, as regards indigenous species, are represented 
by two bats only, though one Pteropus aldabranus is peculiar. 
Reptiles comprise the Giant Land Tortoise (Testudo daudinii), 
the Green Turtle (Chelone mydas), the Hawksbill (Chelone 
imbricata), two species of Gecko and a Skink. The distribution 
of the Giant Land Tortoises affords an interesting problem. They 
have been found in recent times on the Seychelles, the Mascarenes, 
Madagascar, Aldabra, Assumption and Cosmoledo. Their presence 
on continental islands such as the Seychelles is easily accounted 
for by the previous land connection, but this explanation will 
not apply to islands of purely oceanic origin such as Aldabra. 
The fossil bones on the latter atoll appear to prove that they 
do not owe their distribution to transport by man : they are at 
present too large to drift on wreckage or logs, or if drifted before 
their large size was evolved, then they present a wonderful case 
of parallel evolution. The matter still awaits a satisfactory 

Amphibia are absent from Aldabra and the fish though speci- 
fically numerous call for no special mention. 

The land invertebrata are at present being worked out but 
it may be mentioned that the majority seem to be derived from 
Madagascar: indeed it may be said that the whole land fauna 
with the exception of the Giant Land Tortoise is such that it may 
have been obtained from neighbouring lands without necessitating 
any former continental connection. 


Mr Fryer, Aldahra and neighbouring Islands. 

Next passing to the other islands visited, a brief summary of 
the chief structural characters of each may be given. 

Assumption is not an atoll but is an elevated reef composed 
of the same classes of rock as constitute the land-rim of Aldabra. 
The rock is extremely cavernous ; water can penetrate completely 
through the land and there is no doubt that, as the caverns 
inter-connect, the island will be broken up into a number of 

Astove is an elevated atoll with a very perfect land-rim which 
is divided by only one pass. It is composed of the same three 
classes of rock as were found on the land-rim of Aldabra, though 
coral in position of growth is even more common. The lagoon 
is very shallow and probably existed almost entire at the time of 
elevation. It is getting larger ; fresh passes are forming and the 
atoll will be speedily broken up. 

Gosmoledo is also an elevated atoll but differs from Aldabra 
and Astove in having but half its circumference capped with land. 
The remainder, the reef, is elevated coral rock cut down to low 
tide level and piled with coral debris while the edge is protected 
by growing lithothamnia. There is no doubt however that once 
the whole circumference of the rim was land. Sand derived from 
disintegrated rock is abundant and hides the rock of the islands 
so that there is a tendency as the rock land is removed to replace 
it by sand cays. 

The state of Cosmoledo must be considered as forecasting in 
part the future condition of Aldabra, and in conclusion an hypo- 
thetical biography of the latter atoll may be given, basing the 
account on the facts obtained from the various coral islands in the 

The geology of Aldabra shows that it is entirely of oceanic 
origin and has been built up by active coral growth, and therefore 
our history of the atoll must begin with its formation as a reef 
beneath the sea. There must first have been, however, some 
base or mountain-top which reached to within 40 fathoms of the 
surface, for it is well known that reef-building corals cannot 
live at greater depths. Of the nature of this base we have no 
evidence, though it may be taken as probable that it is of the 
nature of a volcanic mound. We know of volcanoes in the 
Comoros to the S.W. and the Sealark dredged volcanic mud near 
Providence to the E., and there is thus no inherent improbability 
in the existence of volcanic action in between. However this may 
be, it is necessary to assume the presence of some base, colonised 
by corals, forming a reef which gradually grew up until it nearly 
reached the surface. This may be deduced from the fact that 
the fossil corals are all of a shallow-water facies. As to the form 
of the reef we suppose both from the geology and from theoretical 

Mr Fryer, Aldabra and neighbouring Islands. 345 

considerations that the outsides were flourishing, while the inner 
portions were but feebly growing or dead. This means that the 
shape of the reef was probably that of a shallow basin. 

The next point in its history was its elevation above the 
surface of the sea, though how this occurred is somewhat doubtful. 
It would naturally be supposed that it was accomplished by 
a slight local elevation of the earth's crust, but against this is the 
objection that there is evidence of an elevation of equal amount 
throughout the western Indian ocean, and it is difficult to conceive 
of an alteration in the level of the earth's crust which would be 
so uniform over such a large area. The only alternative is an 
alteration in the level of the sea, and it may be mentioned that 
there are points in favour of this hypothesis though they are 
of too indefinite a nature to bring up for discussion in this 

The extent of the elevation may be placed at about 60 ft., 
for Esprit island is 30 ft. high, and it is probable that the reef 
hardly reached the surface before elevation, while since then an 
enormous amount of denudation has occurred. After elevation 
the whole reef was placed out of water and the depression in 
the centre was dry. In Astove it will be remembered there was 
evidence that the present lagoon was largely existing before 
elevation, and may therefore be called a primary lagoon, while 
in Aldabra we now see that the present lagoon must be a 
secondary lagoon developed after elevation. The question of its 
formation will be dealt with shortly, but first certain deductions 
must be made from Esprit island which consists almost entirely of 
calcium phosphate. The phosphoric acid was undoubtedly derived 
from guano, and to have formed the phosphate rock on Esprit it is 
necessary to suppose that a solution obtained entrance to a large 
underground cavern which may have contained a certain amount 
of sand or mud. The whole space was gradually filled with the 
deposit, and to have obtained such a large quantity it is necessary 
to suppose that the top of Esprit was the sink or drain from 
a large area covered with guano. This area was probably the 
primary lagoon which after becoming dry was filled with guano 
by oceanic birds. For the present, therefore, it is supposed that 
all the peculiar phosphate rocks of Aldabra were formed by a 
solution of guano obtaining entrance to a subterranean pocket. 

Turning next to the formation of the secondary lagoon, 
mention was made of the fact that the rock as a whole is still 
very cavernous so that water can penetrate completely through 
the land-rim. At the time of elevation this feature must have 
been more marked, and therefore the sea could at once begin 
dissolving away rock and enlarging any spaces. Simultaneously 
rain-water denudation was acting on the surface and the natural 

VOL. XV. PT. IV. 23 

346 Mr Fryer, Aldahra and neighbouring Islands. 

result was a gradual decrease in level. In time the subterranean 
caverns, becoming larger, joined each other and finally a series, 
probably in the neighbourhood of Grande Passe, obtained open 
connection with the sea. After this a tidal current swept in and 
out continually dissolving away rock and forming a lagoon. The 
transition from this stage to the present one is easy : a further 
pass, Passe Houareau, next formed and the lagoon gradually 
obtained its present dimensions, though He Esprit, on account 
of its being composed of an insoluble rock, was left standing as 
a clue to former conditions. The level of the land gradually 
decreased by rain-water denudation and fresh passes continued to 
form until the present state of things obtained. As to the future 
we may safely prophesy the formation of more passes : lagoon 
erosion will proceed with increased speed though it is noticeable 
that land is only cut down to low tide mark, for below this 
lithothamnia, corals and the piling of sand form a protection 
against speedy erosion. Looking further into the future and 
bearing in mind the present state of Cosmoledo we see that 
the rock islands will gradually be divided up and be separated 
from one another by long stretches of reef. The islands may 
be eaten away until no land remains, though it is more probable 
that it will continue to exist in the form of sand cays so character- 
istic of many atolls. This stage may be called the Farquhar* stage. 
Beyond this it is impossible to foretell ; and in conclusion it may 
be suggested that the life-history of Aldabra will be found typical 
of most coral rock islands, and finally may give a clue as to the 
former history of many of the coral sand islands so common in the 

* Farquhar atoll, 150 miles east of Astove, is in this condition. Vide Trans. 
Linn. Soc, Vol. sii. p. 144. 

Plate XII 



Spot t l,at. y-w'J. :i'. S._ Louy. i(i"l4''li"K 

VVtnofi/i/i in. IDO^.tirrrrtuinff abouL B'tumvaUy. 

land f}.^. p.,S'. Champignon Rock and Pemphis Scrub, 
le dott< 

PkiL Soc Pi\x\ XV. Ft. iv. 

Plate XII 

-^^^aiiji— -jifj^i^^^^, j^v^^i^^j^ 


,% This s-i"'!' »'l at-oo.t J- 

*CocoanulT,^v" J'. 



\ : 


All soundint's in fatliouis 

Figures ou the land show the heights in feet above H. W. Springs. 

Double dotted line = a main track, other tracks not indicated. 

crl. coral, r. rock, ,s. sand, .«/(. shells, ji\ white. 

Single dotted line defines an area of land or lagoon. 

R. P.S. Champignon Rook and Pcniphis 


Mr Lillie, Notes on the Larger Getacea. 347 

Notes on the Larger Getacea. By D. G. Lillie, B.A., 
Hutchinson Research Student of St John's College. (Com- 
municated by Mr A. E. Shipley.) 

[Read 22 November 1909.] 

The establishment of whaling stations within recent years in 
three localities off the shores of the British Isles should give a 
new impetus to the study of Cetology, and stimulate additions to 
our knowledge of the larger Cetacea before these much-hunted 
animals become too scarce. 

Hitherto our studies of these enormous creatures have been 
chiefly derived from isolated specimens stranded from time to 
time in various localities around the coasts of civilised countries, 
which coming by chance into the hands of zoologists, often in 
an advanced state of decay, have enabled them to add a few 
observations to the large though scattered Cetacean literature. 
This would indeed seem the only method possible since, during 
the last three centuries, the whaling industry has been confined 
to the wildest regions of the earth and carried on under conditions 
of physical privation which were beyond the endurance of all but 
a few. 

Since the whaling industry of to-day now supplies fresh 
material fairly near at hand, and is destined to play a large 
part in any new work which may be done on the histology and 
general biology of whales in the near future, it will not be in- 
appropriate here to briefly trace the history of this industry from 
early times until its establishment near our shores at the present 
day, and to give a short account of modern methods of whaling 
before proceeding to record an observation of more strictly 
scientific interest, which was made during a preliminary visit 
to the Irish whaling station in the past summer. 

In very early times whales occasionally became stranded just 
as they do now, through venturing too near the shore and being 
left high and dry by the tide. It was, no doubt, soon discovered 
that the oil of these stranded individuals could be utilised ; but 
the practice of pursuing and killing large whales, as far as is 
known, only dates from about the year 875 A.D.j the Basques 
then hunted Balaena hiscayensis, and from their word " arpoi," 
which means " to take quickly," we get the word " harpoon." At 
first the Basques attacked this whale from the shores of the Bay 
of Biscay ; but they later put out to sea on long voyages as the 
quarry became scarcer. 

This fishery was practically exhausted by 1607 when Henry 
Hudson made his first voyage to Greenland and Spitzbergen and 
discovered the Greenland whale (Balaena mysticetus) in its home 


348 Mr Lillie, Notes on the Larger Getacea. 

among the northern icefields. The English and Dutch immediately 
opened up the Arctic whale fishery, taking with them the hardy 
Basque seamen to act as their instructors. This fishery reached 
its height at the beginning of the 18th century, English, Dutch, 
Germans, Spaniards and Danes all taking part. In 1749 the first 
vessels set out from Scotland and took over the fishing in Davis 
Strait, while the Americans worked that of the Behring Strait, 
the fishery on the east coast of Greenland being then exhausted. 
The last great names associated with the Greenland fisheries are 
those of Scoresby and David Gray in the Atlantic and Scammon 
in the Pacific. The fishery is now almost extinct. 

In 1712 the Sperm whale (Physeter macrocephalus) was first 
hunted. This fishery was started by Americans on the island of 
Nantucket in the Atlantic. British ships took part in 1775 and 
extended the fishery to the Pacific and Indian oceans, but they 
abandoned it in 1853. This whale is now chiefly hunted by 
Americans and Norwegians. 

The shore-loving Californian Gray whale {Rhachianectes glaucus) 
was first pursued on the Pacific coast of North America in 1846. 

In 1866 a new era began in the whaling industry. Up to this 
date attention had necessarily been confined to the two species of 
Balaena, the Sperm whale and the Californian Gray whale. All 
these slow-moving creatures could be hunted with the hand 
harpoon in small boats each manned by six men, which put 
out from the shore or from a whale ship in mid-ocean as soon 
as a whale was sighted. 

The fast-swimming Balaenopteridae or Rorquals remained 
unmolested by man until 1866, when Captain Svend Foyn, a 
Norwegian seaman, invented a harpoon which made their capture 
possible. This deadly projectile is fitted with an explosive shell 
and is fired, together with the attached harpoon-rope, from a gun 
in the bow of the whaling steamer. Captain Foyn took out a 
patent for his invention, established a station at Vadso and opened 
up the Rorqual whale fishery off the coast of Finmarken. 

In 1882 his patent expired and numerous stations sprang into 
existence along the northern coasts of Norway and Lapland, after- 
wards spreading to Iceland and the Faroe Islands. 

In 1903 this industry reached the shores of Scotland. There 
are now four stations on the mainland of Shetland and one in 
North Harris in the Hebrides. In 1908 a station was established 
on the Island of South Innishkea off the coast of Co. Mayo in the 
west of Ireland and a second Irish station is expected to open next 
summer. All the stations on the east side of the Atlantic are in 
the hands of Norwegians who, like the old Basque whalers before 
them, are the masters of the industry they invented and have 
been engaged by other nations to teach them their craft. The 

M7^ Lillie, Notes on the Larger Cetacea. 349 

result has been that modern whaling centres have sprung up in 
Newfoundland, Japan and elsewhere. 

The staple quarry of the northern whale fishery is the widely 
distributed family of the Balaenopteridae, the last of the larger 
Cetacea, the Sperm whale and Balaena hiscayensis being also taken 
when they can be found. The Balaenopteridae are still fairly 
plentiful but, at the present rate of slaughter and with the 
rapid spread in the use of the deadly Svend Foyn harpoon, the 
day of their extinction cannot be far distant, as Mr Shipley pointed 
out in his presidential address to Section D at the Winnipeg 
meeting of the British Association. 

The Norwegian method of whaling is briefly as follows. A 
station is established on shore or afloat to which three or four 
strongly built steamers from 15 to 90 tons burden are attached. 
Each has a harpoon gun mounted in her bows. These go to sea 
in search of whales and stay out from two to ten days at a time. 
When a steamer gets within 40 yards of a whale the harpoon is 
fired, and the shell at the point of the harpoon is so arranged that 
when the harpoon enters the body of the animal it bursts and the 
animal is generally killed at once ; but this is not always the case. 

Mr Southwell records an instance of a whale, Balaenoptera 
sihhaldii, towing a Newfoundland whaling steamer for a distance 
of 122 miles, the screw being reversed at full speed the whole 
time. After a pursuit which lasted 26 hours the animal was 
exhausted and killed. 

The Balaenidae and Physeter float when dead; but the 
Balaenopteridae always sink, probably on account of their having 
less oil. The Norwegians have overcome this difficulty by an 
ingenious device. The dead whale is brought to the side of 
the steamer and inflated with air. An iron pipe is thrust into 
the body cavity and is connected by india-rubber tubing to a 
pump in the engine-room. When sufficient air has been pumped 
into the body cavity to render the animal buoyant, the pipe is 
withdrawn and the wound is plugged with a piece of tarred wood. 
In this condition the dead whale is kept afloat, and several can be 
towed to the factory at one time by a whaling steamer. The air 
thus pumped in keeps the carcase distended until it is landed and 
ready to be cut up, its volume being sometimes added to by the 
gaseous products of decomposition. As soon, however, as the dis- 
tended body is pierced by the flensing knife the imprisoned air 
escapes with great violence and portions of the viscera are torn 
away and shot out of the body cavity. The two foetal whales 
which I obtained this year at the Irish whaling station were 
extracted in a mutilated condition from among the scattered 
remains of organs thus expelled from the body cavities of their 

350 Mr Lillie, Notes on the Larger Cetacea. 

Directly a whale is hauled up the slip or landing stage the 
whalebone and the blubber are rapidly stripped off and the latter 
boiled to extract the oil. The remainder of the carcase is dragged 
asunder by means of wire ropes and steam winches and cut up by 
many hands. The bones and soft parts are roughly separated, 
dried and ground in mills to form bone manure, flesh manure, 
cattle food and, at some stations, various forms of preserved meat 
for human consumption. In this way a whole animal 70 feet long 
and as many tons in weight will often disappear completely in the 
course of a morning. 

To the scientific man a whaling station does not pretend to 
offer the advantages of unlimited time and comfort which are to 
be found in a laboratory. It is so essential, in the whaling trade, 
to dispose of the animals as rapidly as possible while the oil is 
fresh that the whalers can hardly be expected to wait for the 
deliberations of the anatomist. Yet there can be little doubt 
that to visit a whaling station such as the one in the west of 
Ireland is a more satisfactory method of increasing our knowledge 
of the larger Cetacea, than to depend upon the occasional stranding 
of an isolated specimen on some part of the coast. For at a 
station all the largest whales, with the exception of Balaena 
nii/sticetus and Rhachianectes glaucus, can usually be seen within 
the space of three months. Very frequently several individuals 
of different species can be examined and compared as regards 
their external characters and their internal characters also, 
according to the skill of the investigator in overcoming the 
obvious difficulties arising from the manipulation of such large 
creatures. The material is often sufficiently fresh for histological 
study, which, on account of the gigantic size of the animals, should 
prove of considerable interest. Moreover exceptional opportunities 
occur for observing the animals in the living state. 

With regard to the smaller Cetaceans, since they are seldom 
killed by man, material is difficult to obtain ; but the study of 
these animals is not at the moment so pressing as that of the 
rapidly decreasing larger forms. 

It now remains to briefly record one of the several observations 
which were made at the Irish whaling station, during a visit of 
seven weeks, in the past summer. 

The distribution and significance of the scanty hairs of the 
Cetacea do not appear to have been hitherto studied in the detail 
they deserve. They have been vaguely referred to as occurring on 
the lower jaw of some adult forms. Sometimes they have been 
found on the foetus only. 

In two adult Sperm whales {Physeter macrocephahis) seen at 
Innishkea this summer, no trace of hairs could be found on any 
part of the animals even after careful searching. 

Mr Lillie, Notes on the Larger Cetacea. 351 

In the case, however, of the Rorquals Balaenoptera sihhaldii 
and Balaenoptera musculus some ten individuals of each species 
were examined and it was found that a definite distribution of 
hairs could be made out in each case. Four rows of white, bristle- 
like hairs from half an inch to an inch in length occur on the 
dorsal surface of the beak or facial region of the head. These 
consist of two inner rows on either side of the median ridge which 
bears the blowholes or external nares and two outer rows following 
the edges of the snout, from points just behind the blowholes to 
its anterior extremity. The average number of hairs in each row 
is about eight. 

On each side of the lower jaw there was a row of some five or 
more hairs running from the tip of the mandible along the middle 
line of the outer edge of each ramus to a point just in front of 
the eye. At the extreme anterior end of the mandible, over the 
ligamentous junction of the rami, there were also two rows of hairs 
set at right angles to those above mentioned. These occur close 
together and run parallel to each other from the upper to the 
under surface of each ramus. The hairs in these two rows are 
placed closer together than in the others, there being generally 
about fourteen hairs in each row. 

On looking through the Cetacean literature there appears to be 
no record of the occurrence of hairs in the odontocetes, except in 
some foeti. It would seem that the presence of hairs in the adult 
is restricted to the whalebone whales and their retention and 
distribution over the beak and mandible in these forms may 
be due to their possessing a tactile function and thus serve to 
indicate to the animal the presence of its food. 

The small size of the organisms, which generally form the food 
of the Mystacoceti, making them difficult to see, and the olfactory 
organs of the Cetacea being very reduced, it seems reasonable to 
suppose that the occurrence of tactile hairs over the oral region 
would be a distinct advantage, as the small food animals would 
brush against them and thus inform the whale when to open its 
mouth. The top of the snout of a whale is, after all, only the 
prolonged upper lip, where one would naturally look for vibrissae. 
The food of the odontocetes being of a larger size the presence of 
tactile hairs is not obviously required, and so the hairy covering 
has entirely disappeared in the adult forms of these whales. If 
the hairs of the whalebone whales do not function as suggested 
above, an interesting problem remains open to solution to explain 
how these animals become aware of the presence of their food. 

352 Mr Southerns, Eocperimental Investigation as to Dependence 

Experimental Investigation as to Dependence of the Weight of 
a Body on its state of Electrification. By L. Southerns, B.Sc. 
(London), Whitworth Scholar, 1851 Exhibition Scholar. (Com- 
municated by Professor Sir J. J. Thomson.) 

[Received 9 December 1909.] 

In a previous paper* the writer described an experiment 
designed to detect any alteration which might occur in the weight 
of a body when its temperature was changed. The present paper 
deals with an experiment which seemed naturally to follow the 
former one, viz. an attempt to detect change of weight due to 
electrification. This experiment, unlike the other, appears to give 
a positive result. The object of the experiment is not to actually 
weigh electricity, but rather to find whether the presence of 
electricity on a body modifies in any measurable degree the force 
of gravity acting upon it. While such a modification of gravity 
seems to provide the simplest way of explaining the results, such 
explanation is by no means insisted upon. Further reference to 
this matter will be made in the last section of the paper. 




Fig. 1. 

The paper is divided into the following sections : 

(1) General theory and method of experiment. 

(2) Description of apparatus. 

(3) Detailed description of experiments and results. 

(4) Conclusion. 

(1) General theory and method of experiment. 

A general idea of the method employed may be gained from 
consideration of fig. ] . 

* Proc. Roy. Soc. A, Vol. lxxviii. December 20, 1906. 

of the Weight of a Body on its state of Electrification. 353 

Suppose a delicately but stably-balanced earthed conductor A 
to be placed between two fixed charged conductors B, G, at 
potentials + F, , - Fg respectively. Two electrostatic fields F^ , F^ 
will be set up, and these will be quite independent of each other, 
provided all lines of force from B to G are intercepted by the 
conductor A, which is at zero potential, or by some other earthed 
conductor. Charges will be induced on the ends of A, which will 
now be subject to electrostatic forces which will in general deflect 
it to a new position inclined at an angle, say 0, from its original 
equilibrium position. If now the fields F^, F^ be reversed each 
independently of the other, so that we have B at potential — Fj 
and G at potential + V^, there will be no change in this deflection 
6 caused by electrostatic forces, for these are independent of the 
direction of the fields. But now let us suppose that a gravitation 
effect exists such as to cause the end of A, which is positively 
charged, to be a little heavier than the negatively charged end. 
This will give a deflection + h which must be added to 6, thus 
with one direction of field we shall have a total deflection 6 -{-h, 
and with the direction of field reversed we shall have deflection 
6 — ^. The difference between the two observed deflections will 
thus be 2S, the electrostatic part of the deflection being eliminated. 
In observing deflections practically two methods may be adopted. 
We may observe the zero position under no field, then put on the 
field in a given direction and observe ^ + S, discharge and re- 
determine zero, then charge in the opposite direction, and observe 
6 — h and take the difference. Or we may disregard the zero and 
merely, having the field in a given direction, observe position of 
A, then reverse the field and note the deflection 28 which results. 
Both these methods have been used. 

It will be seen that there is no theoretical necessity for making 
the fields or the conductors symmetrical or the potentials Fj, V^ 
numerically equal to each other. In practice, however, it is 
desirable to make the apparatus and fields as symmetrical as 
possible, though it is quite possible to obtain results with wide 
differences between the potentials Fj, Fg. With symmetrical 
apparatus the deflection 6, due to electrostatic forces, will be 
small and any deflection due to a gravitation etfect will be more 
readily observed. 

The form of apparatus indicated in fig. 2 is therefore adopted. 
The beam AA with its curved end pieces is supported by a steel 
knife edge and grooved plate by means of which it is electrically 
connected to earth. The pierced guard cylinder D, and metallic 
case E, are also earthed. The field plates B, G are insulated 
and connected through a double reversing key to the sources of 
potential, which are separate for the two plates. Some of the 

354 Mr Southerns, Bocperiinental Investigation as to Dependence 

lines of force from these plates fall on the guard cylinder and on 
the case. The apparatus can be adjusted so that the forces acting 
on AA are very nearly horizontal, so that they produce only a 
very small deflection from the uncharged position. This deflection 
is usually made small for practical convenience, but the resulting 
value of S is the same for large as for small deflections. The 
stability of the arrangement and method of determining sensitive- 
ness while under the electric field will be referred to later. It 
may be mentioned here that variations of weight corresponding to 
5Wo ^^ Towo '^goQ- i^re easily detected in practice. 

This method of arranging the apparatus and of applying and 
reversing the fields eliminates several errors which might be 
expected to cause difficulty in an experiment of this nature. As 
shewn above, the effect of electrostatic forces (which do not depend 

Fig. 2. 

on the direction of the field) is eliminated on reversal. The same 
also applies to any heating effect due to currents which pass while 
charging and reversing, or to leakage currents, and also to electro- 
magnetic effects, none of which depend on the direction of the 
currents or fields. A point which has often been mentioned to the 
writer is the difficulty of eliminating stray lines of force. These 
are really unsymmetrical portions of the field which go to make 
up the deflection 6 as described above and are included in the 
preceding discussion. Experiment shews that great departures 

of the Weight of a Body on its state of Electrification. 355 

from symmetry do not vitiate the result. Thus the field plates 
may be moved, or we may use either of the plates alone, the other 
being earthed, or we may adjust the beam in such a way that d 
is large or small and in either direction from the zero. In all 
these cases the result is unaffected *. In most of the experiments 
the balance was screened from any possible external electrostatic 
effects, this however made no difference to the result — stray lines 
coming on to the beam from the external electrical apparatus gave 
rise to no discrepancy, these will be dealt with more fully when 
the experiments themselves are described. The effects do not 
depend on strict accuracy being attained in the magnitude of the 
potentials employed. A variation of eight volts out of a thousand 
purposely introduced produced no effect on the results. This 
shews that the results are not due to some variation of potentials, 
such as might be caused by contact difference. 

Reference will be made later to some effects observed with 
electrometers which seem to have a bearing on the subject, but it 
should be borne in mind that the present instrument is not an 
electrometer, indeed it is the exact opposite, that is to say it is 
designed so that electric charges produce the least possible de- 
flection instead of the greatest as with the electrometer. 

(2) Description of apparatus. 

The apparatus was for the most partf constructed by the writer 
(who was aided by a Royal Society grant) at the Technical College, 
Huddersfield, and afterwards set up in the Cavendish Laboratory, 
Cambridge. The general plan of the arrangements is shewn in 
fig. 3. 

In the figure, A represents a table standing on rubber blocks 
and supporting the main instrument or balance B which is enclosed 
in a wooden box. C is a table on which are placed an observing 
telescope D, a scale E, with its sliding support and lamp F, a 
double pendulum electroscope G, a multi-cellular voltmeter H, 
keys J, K, L, M, Daniell cell N, and resistance box P, the uses of 
which will be described later. Another table R carries a cabinet 
of 1000 small secondary cells in two separate trays of 500 each, 
which are connected to the key L by the leads T. The diagram 
is approximately to scale, the distance from telescope to balance 
being about two and a half metres. The dotted lines represent 
connecting wires which are insulated on paraffin wax columns. 

* Irregular fluctuations occur in the magnitude of the result, but they are 
extremely small for an experiment of this kind, 
t Knife edges by Oertling. 

S56 Mr Southerns, Experimental Investigation as to Dependence 

Fig. 3. 

of the Weight of a Body on its state of Electrification. 357 

The balance itself is shewn in fig. 4. It is rigidly made so 
that the applied electric forces shall not produce distortion. The 
case, guard cylinder, field plates and beam are constructed of 
magnalium. Referring to the figure, A A represents the beam 
with its arresting arrangements aaa, B one of the end pieces, CG 
the guard cylinder and DE the insulated field plates. The beam 
is electrically connected to the guard cylinder by means of its 
steel knife edge which bears on a grooved steel plate attached to 

Fig. 4. 

a pillar screwed to the guard cylinder. The object of the groove 
in the bearing plate is to prevent side slipping of the knife edge 
under the action of the electric forces. The guard cylinder itself 
is rigidly fixed to the back of the case, and the whole earthed by 
means of the earth wire shewn in fig. 3. (It should be noted that 
all the earth connections are made with one wire as shewn in that 

It will be seen from the figure that a small amount of play is 
allowed between the piece B and the guard cylinder. This allows a 

358 Mr Southertis, Ewperimental Investigation as to Dependence 

few lines offeree from D to pass between the two, and some of these 
will terminate on the edges of B. Those falling on the upper and 
lower edges in the figure give rise to forces tending to deflect the 
beam. If everything is symmetrical these forces will be equal 
above and below, and therefore the beam will not actually be 
moved. But if B is slightly higher than its central positioo, the 
lower gap will be wider than the upper one and more lines of 
force will therefore fall on the lower edge of B than on the 
upper edge. These will tend to bring B back again to its central 
position. The beam is always in stable equilibrium under the 
action of the field. The application of the field, however, affects 
to a slight degree the sensitiveness of the apparatus as a balance, 
and it is therefore necessary to have some means of determining 
the sensitiveness while the field is on. This is provided by the 
arrangement shewn in the upper part of the figure. It is an 
adaptation of a method employed in a balance designed by 
Dr Hicks and used by the writer in the research previously alluded 
to. A small and feeble magnet is attached to the beam as shewn 
by the dotted lines at F. This can be attracted or repelled by a 
small current passing round the coil 0. The deflection produced 
by a given current can be compared once for all with that pro- 
duced by moving a rider a certain distance along the bar H. By 
observing the deflection produced by this current during an actual 
experiment with the plates charged, the sensitiveness can be 
determined, and the value of any deflection produced by the 
charges expressed in mgms. of weight. The current is not of 
course allowed to pass during actual observations. The current 
required to produce a measurable deflection of the beam, though 
small, is vastly in excess of any possible leakage current between 
the field plates in the balance, and therefore it is impossible that 
these should act directly on the magnet and give rise to any 
difficulty by causing deflections. The cell, resistance and key, 
N, P and M in fig. 3, are used for supplying the current. The 
rider is not moved during a series of observations. It is used 
before observations are commenced in order to level the beam. 
By suitably levelling the beam the electrostatic deflection 6 may 
be varied at will, both in magnitude and direction. Many values 
of this deflection have been used in the experiments. 

The deflections are observed by telescope and scale, and a 
double suspension mirror, the position of which is indicated by the 
circle K. The field plates D, E are insulated by sulphur plugs 
and have various adjustments not shewn on the figure. Other 
details, such as knife edge adjustments, etc., are also left out of 
the figure to avoid complication. The front and back of the case 
are of thick magnalium with plate glass windows. The latter 
have been covered inside with tinfoil in the later experiments. 

of the Weight of a Body on its state of Electrification. 359 

with the exception of a small space for observing the mirror K 
which has been closed in with a grid of fine wire. The results, 
however, are exactly the same whether the windows are covered 
or left bare. The whole apparatus is enclosed in a box of wood 
2 inches thick and provided with double windows of plate glass. 

The diagram is approximately to scale. The diameter of guard 
cylinder is 14-3 cms., distance between this and field plates 3 mms., 
the end pieces B, which are square with rounded corners, 4'9 cms. 
square. Weight of end pieces about 28grms. each, total weight 
of beam about 260 grms. 

u S 

Fig. 5 is a diagram of the keys K and L of fig. 8. Z is a 
paraffin block with mercury cups and connections as shewn. The 
cups A, B are connected to the negative and positive terminals of 
the top tray of cells and C, D to the negative and positive terminals 
of the bottom tray. E and H are connected to two other cups Q, 
R, which are permanently connected to the electroscopes and to 
the key J in fig. 3 by wires 8, T. The wires U, V to the balance 
can be dipped into the cups Q, R by means of the lever W to 

360 Mr Southerns, Experimental Investigation as to Dependence 

which they are attached. The cups F, G are permanently earthed 
by the wire X. By means of a rocker not shewn in L connections 
can be made as shewn by the dotted lines, two kinds of dots being 
used to shew the connections corresponding to the two positions 
of the rocker. The mercury in the cups B, G, iV, is higher than 
that in the other cups in order that earth contacts shall always be 
made before and broken after high potential contacts. It will be 
seen that the key simply consists of two ordinary six cup reversing 
keys fastened together. The lever W is used to throw the balance 
connections in or out as desired. It will easily be seen that the 
arrangement here described satisfies the condition that the two 
fields Fj^, F2 of fig. 1 shall be quite distinct from each other. By 
means of the key J in fig. 3 the multi-cellular voltmeter H can be 
connected to either of the wires S, T in fig. 5 at pleasure. 

(3) Detailed description of experiments and results. 

The several experiments will now be described in order and 
their results afterwards discussed. 

1. June 9th, 1909. (Used 1000 volts on each side of balance 
in all cases except when otherwise stated.) There was very large 
electrostatic deflection 6, no attempt being made to reduce this. 
The zero of balance was altering rapidly. In the following tables 
the observations are numbered, and the arrows shew the position 
of the rocker of reversing key (refer to fig. 5), The column 
marked 28 is calculated from three successive readings, it is the 
difference between the mean of the first and last of the three and 
the intermediate reading. 

A. Front cover of balance off. 



Eeadings used for 
calculation of 25 


1 48-2 
3 49-1 
5 51-1 

2 47-4 
4 48-9 
6 50-8 

1, 2, 3 

2, 3, 4 

3, 4, 5 

4, 5, 6 


Mean 1-16* 

See Table on p. 369 for values of 5 corrected for sensitiveness. 

of the Weight of a Body on its state of Electrification. 361 
B. Front cover of balance off. 



Eeadings used for 
calculation of 25 



2 57 
4 58-8 
6 59-6 

1 55-5 
3 56-8 
5 58-0 

1, 2, 3 

2, 3, 4 

3, 4, 5 

4, 5, 6 


Mean M4 

C. Cover on. (The larger windows are coated with tinfoil.) 



Eeadings used for 
calculation of 25 


1 80-2 

2 80-0 

1, 2, 3 


3 82-5 

4 82-2 

2, 3, 4 


5 84-2 

6 83-9 

3, 4, 5 


7 86-0 

8 85-2 

4, 5, 6 


5, 6, 7 


6, 7, 8 

Mean 1-28 

2. June 10th. 

A. Electrostatic deflection large, but not so large as in last 




Eeadings used for 
calculation of 25 


1 67-0 
3 66-5 
5 66-2 

2 66-0 

4 65-6 

6 65-3 

1, 2, 3 

2, 3, 4 

3, 4, 5 

4, 5, 6 


Mean 0-74 



362 Mr Southerns, Experimental Investigation as to Dependence 
B. Taken at 1 minute intervals. Reversed at | minutes. 



Eeadings used for 
calculation of 25 


1 65-9 

2 64-9 

1, 2, 3 


3 65-5 

4 64-9 

2, 3, 4 


5 65-6 

6 64-8 

3, 4, 5 


7 65-7 

8 64-9 

4, 5, 6 


5, 6, 7 


6, 7, 8 

Mean 0-75 

C. Smaller electrostatic deflection, zero for no field 120'0 about: 



Eeadings used for 
calculation of 23 


1 17-4 

2 14-9 

1, 2, 3 


3 15-1 

4 13-3 

2, 3, 4 


5 13-9 

6 12-2 

3, 4, 5 


4, 5, 6 

Mean 1-17 


Cut out and earthed balance, and moved over reversing 
key several times. No change of zero. 

3. June 12th. 

A. Taken at 1 minute intervals. Zero about 63'0. 



Eeadings used for 
calculation of 23 



2 27-0 
4 25-5 

1 26-9 
3 25-0 
5 24-1 

1, 2, 3 

2, 3, 4 

3, 4, 5 


Mean 1-08 

of the Weight of a Body on its state of Electrification. 363 

B. Put 4 volts in and out of one battery of cells. This 
made no appreciable difference to the deflections. 

C. Zero about 52*5. 



Eeadings used for 
calculation of 25 


1 22-8 
3 22-1 
5 21-7 

2 21-2 
4 20-8 

1, 2, 3 

2, 3, 4 

3, 4, 5 


Mean M5 

D. Zero taken between reversals. Observations at 1 minute 






Readings used 
for calcula- 
tion of 25 


1 21-4 

5 21-5 

2 52-4 
6 52-3 

3 20-3 
7 20-2 

4 52-2 

1, 3, 5 

3, 5, 7 


Mean 1-20 

E. Put 4 volts in and out of one battery. The only effect was to 
alter the electrostatic deflection 6 in the ratio 4 : 1000. This 
alteration was about 0"1 scale divisions. 

4. June l^th. 

A. Zero about 60'5. Electrostatic deflection in opposite 
direction to last. 

j gave 72'3 

f gave 7 1*3 (about). 

B. Put 8 volts in and out of one battery, no perceptible 
difference in deflections. 


364 Mr Southerns, Experimental Investigation as to Dependence 
C. Very small electrostatic deflection and zero steady. 





Readings used 
for calcula- 
tion of 25 


1 99-0 

2 100-1 

3 98-8 

4 101-0 

2, 4, 6 


5 98-8 

6 100-0 

7 '98-7 

8 101-0 

4, 6, 8 


9 98-7 

10 100-0 

11 98-5 

12 100-9 

6, 8, 10 


13 98-5 

14 99-8 

15 98-3 

16 100-7 

8, 10, 12 
10, 12, 14 
12, 14, 16 


Mean 0-98 

D. Reversed without taking zero. 



Eeadings used for 
calculation of 25 


1 100-7 
3 100-7 

2 99-8 
4 99-7 

1, 2, 3 

2, 3, 4 


Mean 0-92 

5. June 17 th. Covered all the remaining windows with 
tinfoil, except for a small space for observation of mirror, in this 
and following experiments. 



Eeadings used for 
calculation of 25 


1 127-3 

2 128-3 

1, 2, 3 


3 128-0 

4 128-9 

2, 3, 4 


5 128-7 

6 129-5 

3, 4, 5 


4, 5, 6 


Mean 0-57 

of the Weight of a Body on its state of Electrification. 365 
B. Zero about 7 I'D. Reversed as rapidly as 'possible. 



Readings used for 




calculation of 25 





1, 2, 3 






2, 3, 4 






3, 4, 5 






4, 5, 6 

5, 6, 7 

6, 7, 8 


Mean 0-55 

6. Jime 18th. Reversed connections of balance on the lever 
M. Kept all other connections as before. Effect should be in 
opposite direction to previous effects, which is the case. 




Readings used for 
calculation of 25 


1 82-5 

2 81-9 

1, 2, 3 


3 82-5 

4 81-7 

2, 3, 4 


5 82-1 

3, 4, 5 

Mean 0-63 

7. June 19th. Balance connection reversed as yesterday but 
only one side of balance used, the other being earthed. Should 
give half previous effects. 

A. Left side of balance used. Observations at 1 minute intervals. 



Readings used for 
calculation of 25 


1 107-0 



1, 2, 3 


3 106-2 



2, 3, 4 


5 105-6 



3, 4, 5 

4, 5, 6 


Mean 0-24 

366 Mr Southerns, Experimental Investigation as to Dependence 
B. Right side of balance used. 



Keadings used for 

calculation of 25 



1 111-3 

2 110-8 

1, 2, 3 


3 111-2 

4 110-5 

2, 3, 4 


5 111-0 

6 110-2 

3, 4, 5 


4, 5, 6 

Mean 0-56 

8. Jidy 10th. Balance connections in normal position. 

A. 1000 volts each side as usual. Observations at 1 nninute 




Readings used for 
calculation of 25 


1 103-2 



1, 2, 3 


3 102-2 



2, 3, 4 


5 101-2 



3, 4, 5 

4, 5, 6 


Mean 1-29 

B, 660 volts each side. 



Readings used for 
calculation of 25 


1 103-3 

2 103-8 

1, 2, 3 


3 102-1 

4 102-7 

2, 3, 4 


5 101-1 

6 101-7 

3, 4, 5 


4, 5, 6 


Mean Ml 

of the Weight of a Body on its state of Electrification. 367 

C. 330 volts each side. 



Readings used for 
calculation of 25 


1 103-3 

2 103-3 

1, 2, 3 


3 1020 

4 102-0 

2, 3, 4 


5 100-7 

6 100-7 

3, 4, 5 


4, 5, 6 

Mean 0-65 

9. July \Qth. 800 volts. Right plate of beam covered 
(except near edges) with shellac varnish. That side of balance 
only used, the left side being earthed. 



Readings used for 
calculation of 25 


1 14-5 

2 14-0 

.1, 2, 3 


3 14-3 

4 13-8 

2, 3, 4 


5 14-0 

6 13-3 

3, 4, 5 


4, 5, 6 


Mean 0-40 

Corrected to"! ^ ^^ 
1000 volts 1^'^'-' 

868 Mr Southerns, Experimental Investigation as to Depeoidence 

10. July 19th. Used left side only. A wire was passed 
through case and bent inside into proximity with the field plate 
and end piece of beam, but without touching them. This could 
be connected to one terminal of a Daniell cell, the other terminal 
being connected to balance case. 

A. Wire not connected to cell. 



Readings used for 




calculation of 25 



1 7-2 

2 6-8 

], 2, 3 


3 7-2 

4 7-0 

2, 3, 4 


5 7-3 

6 7-0 

3, 4, 5 


7 7-2 

8 6-9 

4, 5, 6 


9 7-3 

5, 6, 7 


6, 7, 8 


7, 8, 9 


Mean 0-30 

B. Wire connected. 



Readings used for 
calculation of 25 


1 7-2 

2 6-9 

1, 2, 3 


3 7-2 

4 6-8 

2, 3, 4 


5 7-2 

6 6-8 

3, 4, 5 


4, 5, 6 

Mean 0-36 

of the Weight of a Body on its state of Electrification. 369 

Summary of Results, corrected for Sensitiveness. 

Number of 

Deflection 25 




1-0 div. 

= x mgms. 





value of 


1. A. 

scale divs. 




very large 


2. A. 





3. A. 





4. C. 



+ 1 


5. A. 



+ 54 

+ 54 


6. A. 



+ 42 


7. A. 



+ 22 


8. A. 







9. A. 



very large 



10. A. 




* The values of 5 in experiments 7 — 10 are not directly comparable with the 
previous values, as various charges were used, as described above, in those experi- 


370 ilir Southerns, Experimental Investigation as to Dependence 

It will be seen from the above results that a positive effect 
is constantly exhibited, constant in direction and as uniform in 
magnitude as can be expected when regard is had to the nature of 
the experiment, and the fact that the effect only represents a 
difference of a few ten thousandths of a milligramme. Indeed it 
is surprising that the fluctuations are not much larger. Some 
preliminary experiments, in which the sources of potential were 
charged Leyden jars, gave similar results, though they were more 
irregular on account of the leakage of the jars. They shewed, 
however, that changes in the adjustment of the apparatus which 
were constantly made, had no influence on the average values of 
the results. 

From Experiment 8 J., i?, C it will be seen that the effect — 
so far as measurements of the actual magnitude can be relied on 
— is proportional to the induced charges or to the potentials of the 
field plates. 

A few possible sources of error may be briefly alluded to : 

1. External electrostatic action due to lines of force entering 
the balance case from outside. The fact that the front of the 
balance case may be on or off (Experiment 1) or the windows 
coated with tinfoil, or left bare without sensibly altering the result, 
seems to shew that this source of error is inoperative. It is hardly 
possible that it could be otherwise, for electrostatic effects de- 
pending on the external conductors from key to balance would be 
eliminated on reversal, and any permanent field which might exist 
which could send stray Wnes on to the beam, would merely give a 
permanent deflection which would not alter the value of 2S on 
reversal of the fields F^, F^, unless these stray lines penetrated to 
the surfaces of the end pieces where the induced charges resided. 
An examination of the drawing will shew how unlikely this is to 
be the case. Moreover the shape of the surfaces is such that very 
few of the lines so reaching them would tend to deflect the beam. 
If the result had been due to direct action of the cells, voltmeters, 
or other parts of the electrical apparatus, other than the conductors 
mentioned above, it would have changed sign in Experiment 6 
when the balance connections were reversed, but this was not the 

2. Mechanical operation of turning the reversing key. In 
Experiment 6 the result would have changed sign had it been 
caused by this operation. Moving the key produced no disturbance 
of the balance. 

3. Accidental variations in the potentials applied. Actual 
variations of four and eight volts made no perceptible difference 
to the results. See Experiments S B, E, 4^ B. These variations 
were much greater than any which could have occurred during the 
majority of the experiments. 

of the Weight of a Body on its state of Electrification. 871 

4. Small permanent fields inside the balance case. The 
remarks under 1. above apply to this case also. In order to test 
directly Experiment 10 was tried, in which a small field was pur- 
posely introduced. The small effect recorded is within the limits 
of experimental error, as an examination of the actual observations 
will shew. Asa matter of fact, no movement whatever of the scale 
could be detected when the field was put in or out. 

5. Surface effects of the pieces carrying the induced charges. 
In Experiment 9 one of the end pieces was coated (except near 
the edges) with shellac, and this end of the apparatus only was 
charged. It was feared that the shellac might give rise to electro- 
static difficulties, but none were experienced, thanks no doubt to 
the approximate symmetry of the apparatus. It is probable that 
the field plate was a little further from the beam than usual in 
this experiment. The result was the same as in Experiment 7 B, 
when the same side of the apparatus was used. The value in 
Experiment 9 is probably a little low (perhaps 1 in 5 or 6) due to 
the suspected increase in the distance between the plates, but 
the similarity of the results shews that these are not caused by 
any peculiar action of the metal surfaces. 

Some other sources of error, such as heating and electro- 
magnetic effects, have already been dealt with. 

(4) Conclusion. 

Whether the effect be due to a modification of gravity or not, 
the experiments appear to shew that a body, positively charged 
with 20 electrostatic units of electricity, behaves as though it were 
heavier than the same body negatively charged, by an amount of 
the order of "0007 mgms. If the effect be due to a change in 
gravity, there will exist in an electrostatic field a small amount of 
energy due to this cause, and this will involve a very slight 
alteration in the configuration of the lines of force from that given 
by ordinary electrostatic laws. This would be so small as to pass 
unnoticed in ordinary cases. It would be such that with given 
conductors charged in a given way and then reversed as to sign of 
charge, we should obtain two slightly different configurations of 
field. Delicate instruments might detect this, and it is possible 
that the different zeros of a quadrant electrometer, with the needle 
positively and negatively charged, and quadrants earthed, may be 
due to this cause, though the writer has not investigated these 
effects, for the explanation of which the above suggestion may be 
quite inadequate. 

It was suggested to the writer that the effects might possibly 
be caused by an accumulation of air condensed on the surfaces 
of the metal, the quantity being greater when the surface was 
positively than when negatively charged. Experiment 9 was 

372 Mr Southerns, Experimental Investigation, etc. 

really made in view of this suggestion, but from the point of view 
of energy it would appear difficult to explain the result in any such 
way as this. For we may liken the metal surface to a series of 
buckets which are filled with condensed air, when the surface is 
charged positively, but empty when it is charged negativelj''. 
Now if we have a number of such surfaces, fixed to spokes, 
radiating from a central axis so as to form a kind of wheel (like 
a water-wheel) and place this between charged field plates, we 
should have all the buckets on one side full and those on the other 
side empty, and the wheel would revolve. It is difficult to see 
where the energy would be drawn from to keep up this rotation. 

It may be of interest, as a mere speculation, to see whether the 
theory of gravitation which supposes that the attraction between 
unlike charges is somewhat greater than the repulsion between 
like charges, could be modified to suit the present results. Let us 
suppose that the repulsion between two positive units at a given 
distance apart is P, and that between two negative units N, and 
that the attraction between a positive unit and a negative unit is 
M. Then the attraction between a neutral body (containing a 
unit of positive and a unit of negative electricity) and a positive 
unit will be M — P, and that between the neutral body and a 
negative unit M—N. The difference between these will be 
N—P, which is the effect found in the experiments. Again the 
attraction between two neutral bodies (each containing one positive 
and one negative unit) will be 2M — (P + N) and this will be 
ordinary gravity. The last expression is much smaller than N—P 
and thus we should have the result that while N and P both differ 
considerably from M, their mean is very nearly equal to M. Since 
in the attraction M one charge of each kind is employed, it is 
perhaps not unnatural to suppose that this might be the case. 
The actual differences between M, N and P would of course be 
exceedingly small in comparison with their absolute magnitudes. 
Assuming M to be the ordinary electrostatic attraction, we have 
two equations for finding iVand P. It should be remembered that 
in the experiment, as in this theory, no lines of force pass between 
the attracting masses. In the experiment the lines do not pass 
to the earth, but sideways to the field plates. Turning aside from 
such hasty speculations, the writer would be most grateful for 
suggestions as to possible sources of error in the experiments, as he 
hopes to have an opportunity of repeating them later with im- 
proved apparatus, the design of which might be modified in view 
of any suggestions thus made. 

In conclusion the writer desires to express his thanks to Sir J. 
J. Thomson and to Professor W. M. Hicks and Dr S. R. Milner 
for valuable criticisms and for the kindly interest which they have 
taken in the experiments. 

Miss Pearson, Note on an Attempt to Detect a Difference, etc. 373 

Note on an Attempt to Detect a Difference in the Magnetic 
Properties of the Two Kinds of Ions of Oxygen. By Miss D. B. 
Pearson. (Communicated by Prof. Sir J. J, Thomson.) 

[Received 11 November 1909.] 

During the past year attempts have been made to discover 
v/hether a magnetic field effects any separation of ionised oxygen 
into its positive and negative constituents. Were such a separation 
detected it would point to a difference in the magnetic properties 
of the two kinds of ions. 

The method of experiment was briefly as follows. Oxygen, 
ionised by passage through a long tube lined with uranium oxide, 
was passed between the poles of a strong electro-magnet and then 
into a Faraday Cylinder connected to a Dolezalek Electrometer. 
At first the gas was driven steadily through the apparatus with 
the electro-magnet not active. The charge going to produce the 
electrometer deflection was then merely that due to the excess of 
one ion over the other, produced by the difference in the rates 
of diffusion of the two kinds of ions. Readings of the rate of 
deflection of the electrometer needle in these circumstances were 
taken. Then the magnetic field was put on across the tube, 
through which the oxygen was passing, and observations of the 
movement of the needle once more made. If one ion were more 
magnetic than the other it would have had a greater tendency 
than the other to get into the region between the pole-pieces 
of the electro-magnet, where the field was strongest. Consequently 
the gas beyond this region would have been poorer in the more 
magnetic ion, and this dearth of one of the charged constituents 
of the gas reaching the Faraday Cylinder would have affected the 
rate of deflection of the electrometer needle. 

As a matter of fact, numerous observations gave no certain 
indication of any effect produced by the magnetic field. All the 
readings were small and variable, both with and without the 
electro- magnet active. The means of the two series of readings 
were, however, so closely concordant that the results may be fairly 
taken to shew that the difference between the magnetic properties 
of the two kinds of ions of oxygen, if it exists, is beyond the limits 
of accuracy of the method used. 

It would be out of place here to discuss in full quantitative 
results, but it will perhaps be well to refer to them shortly. The 
electrometer deflections were of the order of 3'5 scale divisions 

374 Miss Pearson, Note on an Attempt to Detect a Difference, etc. 

per minute whether the magnetic field was off or on. Such a 
deflection was found to be produced if, in the conditions of the 
experiment, 5'5 °j^ more of one ion than the other reached the 
Faraday Cylinder. Although an exact limit cannot be set, it is 
certain that a readjustment of ions sufficient to change the rate of 
deflection of the needle by "5 scale divisions could not have escaped 
detection. The magnetic field used cannot therefore have pre- 

5'5 °/^ ions of either sign from 

escaping beyond it to the cylinder. The magnetic field employed 
was found to be about 6000 gauss at its maximum, and its greatest 
rate of variation was 5000 gauss per centimetre. 

vented more than '8 

= 3^"^ 

Prof. Thomson, On the theory of the motion, etc. 375 

On the theory of the motion of charged Ions through a Gas. 
By Sir J. J. Thomson, Cavendish Professor of Experimental 

[Head 8 November 1909.] 

In the usual method of calculating the velocity of a charged 

ion through a gas, the expression for the velocity is obtained 

on the assumption that the ion after each encounter with a 
molecule of the gas starts afresh and is as likely to move in any 
one direction as the opposite. The momentum communicated to 
the ion by the electric field in the interval before a collision 
is assumed to be transferred to the molecule of the gas during 
that collision, from which it follows that the maximum velocity 
communicated to an ion by the electric field is that imparted 
to it in the short interval between two collisions. It seems clear 
however that the time during which the velocity is acquired 
by the ion is the average time during which the ion continues 
to move in one direction and not the time between two collisions, 
and the time taken for an ion to have its motion reversed by its 
collision with the other molecules may be much greater than the 
time between two collisions. This will certainly be the case if 
the mass of the ion is considerably greater than that of the 
molecules against which it strikes. For let us suppose that the 
average kinetic energy of the ion is equal to that of the molecules. 
Let m be the mass of the ion, u its velocity, M and v the corre- 
sponding quantities for the molecules, then since 

mu- = M'o^, 


__v _ li 

I TTl 

thus the momentum of the ion will be / -rv times the momentum 

of the molecule against which it strikes and so the ion will have 

1 / in 
to collide with at least -^ . ^r molecules before its motion is re- 
^\J M 

versed. From this it would appear that the quantity \ which 

appears in the expression for the mobility of the ion should be, 

not the ordinary free path, which depends only on the size of the 

ions and molecules and not upon their masses, but that free path 


multiplied by some fraction of / -^ ; if we call Xo the ordinary 

free path, the expression for the mobility would be 

e \o Im 
^ mu s/ M' 
where p is o. numerical coefficient which we have not determined. 

376 I*rof. Thomson, On the theory of the motion 

If the absolute temperature is d 

\mu^ = ol6, 

where a does not depend upon the nature of the ion or of the gas. 
Thus the mobility will be 

i.e. it will not depend upon the mass of the ion except in so far as 
mass is an indication of size, and since Xo diminishes on this view 
as the size of the ion increases, \ would depend to some extent on 
the value of m. 

It must be confessed however that in this as in many other 
problems the methods founded on the mean free path leave much 
to be desired, and are far less satisfactory than the method 
introduced by Maxwell when he replaced the idea of collisions 
between hard elastic spheres by that of the effects produced by 
forces exerted by one molecule on another. Maxwell gave a 
complete solution when these forces are repulsions varying in- 
versely as the fifth power of the distance. It happens that on 
the simplest view we can take of the forces between a charged 
ion and a neutral molecule, i.e. that these forces are due to the 
attraction between the electric charge on the ion and the dis- 
tribution of electricity induced by this charge on the molecules 
regarded as conducting spheres, these forces will vary inversely as 
the fifth power of the distance unless the ion gets close to the 
molecule. For the attraction between an electric charge e and an 
unelectrified conducting sphere of radius a is equal to 

(see Thomson's Electricity and Magnetism, 4th edition, p. 154), 
where f is the distance between the charge and the centre of the 
molecule ; when / is a considerable multiple of a, this expression is 


and thus varies inversely as the fifth power of the distance between 
the ion and the molecule. In this case the force is an attraction 
while Maxwell considers the case of a repulsion. Maxwell's 
investigation can be applied to the case when the force is attractive 
with hardly any modification, the only change that is required 
is in the numerical constants which Maxwell denotes by -4i, A^^; 
these have not the same values for repulsion as for attractive 
forces, since they depend on the magnitude of the apsidal 
distance ; with this exception Maxwell's results can be applied 

of charged Ions through a Gas. 377 

without modification to the case when the forces are attractive. 
Maxwell gives an expression for the coefficient of diffusion of one 
gas A into another B of the form 

^''~ ^hV m.^1 

where mj, 'm^ are the masses of the molecules of A and B, v^, v^. 

the number of these molecules in unit volume, K the force at 

unit distance and h = N/2p, where p is the pressure exerted by 

a gas in which there are N molecules per cubic centimetre, 

A = 2 , where A; is a constant and 6 the absolute temperature of 

the gas. A I is a, numerical constant, having when the forces are 
repulsive the value 2"659. Suppose now nii is the mass of a 
charged ion the preceding equation will give us the coefficient 
of diffusion of the ion through the gas, if we change the value 
of Ai to allow for the force being attractive, and put K = 2e^a^, 
where a is the radius of a molecule of the gas B. We can eliminate 
a by means of the relation 


where /X2 is the index of refraction of the gas B when there are 
N of its molecules per cubic centimetre. In the case of an ion 
diffusing through a gas, Vi may be neglected in comparison with V2 
so that 

^ _ 1 /rth+m^ / 


e^{fji2— 1) AiV2 

The mass of the charged particle only enters this expression 
through the term w — ? , thus when the mass of the charged 

particle is small compared with the mass of a molecule of a gas 
through which it is diffusing, the coefficient of diffusion varies 
inversely as the square root of the mass of the ion ; if however 
the mass of the ion is large compared with that of the molecule 
the coefficient of diffusion varies exceedingly slowly with the 
mass of the charged ion. Hence it seems to me that we can 
attach but little value to the determinations of the atomic weight 
of the emanations made by measuring their rate of diffusion 
through air or hydrogen, for if these were positively charged 
heavy particles the rate would be practically the same whether 
the atomic weight of the emanation were 200 or 2000, though 
this objection would not apply to methods based on the diffusion 
through porous plugs. 

378 Prof. Thomson, On the theory of the motion 

The mobility of an ion, i.e. the speed with which it moves 
through the gas under unit electric force, is connected with the 
rate of diffusion of the ion by the equation 


where tt is the pressure due to iV" molecules per cubic centimetre. 

\ mi ma Vyu,2— lilt's 

We see from this that the mass of a heavy ion has not much 
effect on its mobility; the mobility of an ion consisting of a charged 
molecule of the gas through which it is moving is \/2 times the 
mobility of one whose mass is very much greater than that of a 
molecule of the gas ; the mobility does not however depend on the 
charge on the ion. The velocity, through hydrogen, of an ion made 
of a molecule of hydrogen charged with electricity, would be about 
half as much again as that of a charged molecule of methyl iodide 
through hydrogen and so would easily be distinguished from it. 

Mobility of an ion through a mixture of gases. 

If we have a small number of charged molecules A diffusing 
through a mixture of gases B and G we can readily prove by 
Maxwell's method that i), the coefficient of diffusion oi A through 
the mixed gases, is given by the equation 

D^-l 1 

2hA^ / mim.2 lyb^—Y.e^ I niiWis I \x^—\.e^ 

""'V m, + m,\/ SttN '^ "' V m, + m,V irN ' 

where Vq, and v^ are respectively the number of molecules of 
B and G present per unit volume, m^, m^ the masses of the 
molecules of these gases, /ig and fis the indices of refraction 
of these gases when there are N of their molecules per unit 

The mobility k of the ion through these gases is given by 

1 / mjma /fx„—l I vfi-jn-i I ix^ — \ 

Let us consider the application of this equation to the experi- 
ments lately made by Mr Wellisch on the mobilities of the ions 
through mixed gases and calculate the difference between the 
mobilities through the mixture of charged molecules of B and 

of charged Ions through a Gas. 379 

G. Mr Wellisch has proved to a high degree of accuracy that 
in these mixed gases there is only one mobility. Let us take 
the case of O2 and SO2 investigated by Mr Wellisch and cal- 
culate the velocity (1) of an oxygen ion consisting of a charged 
molecule of oxygen, and (2) that of an ion of SO2 consisting 
of a charged molecule of SO2 ; let us suppose that the partial 
pressures due to these gases are the same so that Vi = v^. If rn^ 
is the mass of an oxygen molecule, m^ that of an SO2 molecule, 
nis = 2m2, and /i2 — 1 = '0003, /A3 — 1 = -00066 ; substituting these 
numbers we find that the velocity of a charged oxygen molecule 
through the mixture would be about 15 per cent, greater than 
that of a charged molecule of sulphur dioxide, a difference which 
could easily have been detected in Mr Wellisch's experiments. If 
the ions from oxygen and sulphur dioxide had been much more 
complex than the single molecule of these gases their mobilities 
through the mixed gases would have been much more nearly 
equal than for the simple ions, and the difference in this case 
might have escaped detection. 

We shall consider in the light of the expression given above 
for the mobility the various views that have been taken of the 
nature of the ion. There are two main points to be considered 
with regard to the ion, (1) is the ion more complex in structure 
than a molecule, i.e. does it consist of an aggregation of molecules, 
and (2) can the electric charge on the ion leave the ion and find 
another home, thus producing a new ion, or is the charge bound 
by an indissoluble bond to the molecules forming the ion. It 
would seem clear from the great increase in the mobility of the 
negative ion which takes place in flames that the negative charge 
must be able to leave one ion, exist for a time as a corpuscle and 
then form a fresh ion: the question then is confined to the 
positive ion, and we have to consider whether or not a positive 
charge, carried by something much more massive than a corpuscle, 
can leave one positive ion, unite with a molecule of the gas, and 
form a new positive ion. If there were no transference of charge 
from the positive ion, then if the positive ion was a single 
molecule or even two or three molecules, there would in mixtures 
of gases be two sets of positive ions moving with speeds sufficiently 
different to have been detected in experiments like those made by 
Mr Wellisch. Wellisch made some other experiments where a 
small quantity of methyl iodide was mixed with a large quantity 
of hydrogen, and it was found that the velocity of the positive 
ions (which had originated from the methyl iodide) through the 
mixture was the same as that of the positive ion through pure 
hydrogen when the ion had originated from the hydrogen. If the 
positive ion in hydrogen had been a single molecule of hydrogen 
the velocity of the positive ion in pure hydrogen would be \/2 times 

380 Prof. Thomson, On the theory of the motion, etc. 

the velocity in the mixture instead of being equal to it. We may 
therefore conclude that if there is no transference of the charge 
the mass of the ion must be a considerable multiple of that of the 

We must therefore consider whether the hypothesis of 
complex positive ions is sufficient to explain the results which 
have been obtained as to the mobility of the positive ion. The 
expressions given for the mobility shew that when the mass of 
the ion is large compared with the mass of a molecule of the gas 
through which it is moving the mobility of the ion will be 
independent of the electric charge carried by it, practically 
independent of the mass of the ion, and at constant pressure will 
vary directly as the absolute temperature, and will be inversely 
proportional to the V^n (//, — !), where m is the mass of a molecule 
of the gas through which the ion is moving and fj, its refractive 
index. The result that the velocity is independent of the charge 
and mass of the ion and depends only on the nature of the gas 
through which the ions are moving is not in accordance with the 
results obtained by Professor H. A, Wilson for the mobility of 
ions in salted flames, for he found that the velocity of the 
positive ions when salts of the alkaline earths were placed in 
the flame was but little more than half the velocity of the positive 
ions when salts of the alkali metals were placed in the flame. 
Again though, as Mr Phillips' results shew, the law that the 
mobility at constant pressure is directly proportional to the 
absolute temperature is very approximately obeyed at moderate 
temperatures, it breaks down altogether at temperatures as high 
as those which occur in flames. Thus the experiments of H. A. 
Wilson and Moreau shew that at a temperature of about 2000° C. 
the velocity of the positive ions in flames impregnated with salts 
of the alkali metals is about 60 cm./sec. for a potential gradient 
of 1 volt per centimetre ; the velocity of positive ions through 
air at 0° C. is about 1*4 cm./sec, so that the velocity at 2000° C. 
would if it were proportional to the absolute temperature be 
12 cm./sec, which is only one-fifth of the actual value. The rapid 
increase in mobility with temperature is what we should expect if 
the positive charge could, like the negative, pass from one molecule 
of the gas to another. 



On the Oscillations of Stiperposed Fluids. By H. J. Priestley. (Com- 
municated by W. Welsh.) (One fig. in Text) . . . . 297 

Discontinuities in Light Emission. By Norman Campbell. (Three 

figs, in Text) . . . . . 310 

The emission of positive rays from heated phosfhoms compoimds. By 

Frank Horton. (Two figs, in Text) 329 

On the shape of beams of canal-rays. By J. A. Orange. (Communi- 
cated by Professor Sir J. J. Thomson.) (Seven figs, in Text) . 334 

An Electric Detector for Electromagnetic Waves. By E. M. Welhsch. 
(Communicated by Professor Sir J. J. Thomson.) (One fig. in 
Text) 337 

Aldahra and neighbouring Islands. By J. C. F. Fryer. (Plate XII) . 340 

Notes on the larger Cetacea. By D. G. Lillie. (Communicated by 

A. E. Shipley) . 347 

Experimental investigation as to Dependence of the Weight of a Body on 
its state of Electrification. By L. Southerns. (Communicated by 
Professor Sir J. J. Thomson.) (Five figs, in Text) . . . . .352 

Note on an Attempt to Detect a Difference in the Magnetic Properties 
of the two kinds of Ions of Oxygen. By Miss D. B. Pearson. (Com- 
municated by Professor Sir J. J. Thomson) . . . . . 373 

On the theory of the motion of charged Ions through a Gas. By Professor 

Sir J. J. Thomson 375 





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Camkitrgt |p]^Has0p]^kal Scrmtg. 

On the relative velocities of diffusion in aqueous solution 
of rubidium and caesium chlorides. By G. R. Mines, B.A., 
Fellow of Sidney Sussex College. (From the Physiological 
Laboratory, Cambridge.) 

[Bead 24 January 1910.] 

In the course of some physiological work with the chlorides of 
the alkali metals certain results led me to inquire as to the 
relative rates of diffusion of these salts in aqueous solution. While 
many data are available regarding the salts of lithium, sodium, 
and potassium, I have been unable to find any figures relating 
the two rarer members, rubidium and caesium, to the rest of the 

The method I have used offers certain advantages in the 
simplicity of the manipulations involved and the small quantity 
of material needed for a determination. I therefore publish this 
short account in the hope that it may be of use to others. 
Graham* showed nearly fifty years ago that sodium chloride 
diffuses in a gelatine jelly as quickly as in distilled water. 
Voigtlanderf found that the rate of diffusion of salts in agar- 
agar was unaffected by changes in the strength of the jelly 

from l7o-57o- 

My plan has been to keep a solution of salt of known concen- 
tration in contact with a free surface of jelly, and to ascertain the 
rate of progress of the salt by measurement of the electrical 
conductivity at a fixed distance below the surface of the jelly. 

* Thomas Graham, Phil. Trans. 1861, p. 183. 

+ Voigtlander, Zeitschr. Physik. Ghem, ill, 1889, p. 316. 

VOL. XV. PT. V. 25 

382 Mr Mines, On the relative velocities of difiusion in 

The apparatus employed for this purpose is depicted in fig. 1. 
It consists of a resistance cell of special shape. The platinum 
electrodes are fused into opposite points in the wall of a glass 
tube fifteen centimeters long and thirteen millimeters in internal 
diameter, about twenty-two millimeters from the lower end, 
which is sealed. During an experiment the mouth of the tube is 

Fig. 1. 

closed by a cork pierced b}^ a short tube in which slides the glass 
plunger P. This is prevented from turning by the piece of 
cork G, which, gripping the plunger and sliding loosely on the 
rod R, acts as a guide. The plunger is raised and allowed to drop 
every two minutes by a wheel moved by clockwork and having 
two pins projecting from opposite spokes in the same direction as 
the axis. 

aqueous solution of rubidium and caesium chlorides. 383 

Five cubic centimeters of a warm 47o solution of well washed 
gelatine* were introduced by a pipette and allowed to solidify. 
The cell was immersed in a water bath kept at 18° C. The 
resistance of the jelly was determined by the telephone method, 
using a post-oflSce resistance box ; the alternating current was led 
off from the primary of a small induction coil, the secondary being 
connected in series with a 10 c.p. lamp to the 50 volt, 90 '^, house 
supply. ^ 

The resistance of the jelly was not affected by standing m 
contact with distilled water for over three hours : it is therefore 
certain that the progressive changes in conductivity observed when 
salt solutions are substituted for the water are not complicated 
by the diffusion of impurities away from the gelatine. The salt 
solutions used were deci-normal. 10 c.c. of the solution were 
poured on the jelly, filling the cell to the level indicated in the 
figure, and the resistance of the gelatine between the electrodes 
was measured, usually at intervals of half an hour, for the next 
eight or ten hours. 

The specific conductivity was obtained for each reading by 
dividing the constant for the cell (•643) by the resistance in ohms. 
From this the specific conductivity of the gelatine at the beginning 
of the experiment was deducted, the result indicating the specific 
conductivity due to the salt. The molecular concentration of the 
salt corresponding to each of these values was read off from curves 
constructed from the figures given by Kohlrausch-f" and his co- 
workers. At the dilutions with which we are concerned the 
specific conductivity is very nearly in linear proportion to the con- 

On plotting the concentrations against the times from 
the beginning of the experiment the curves were found to be at 
first convex to the base line and towards the end of the experi- 
ment slightly concave, but in every case over a period of at least 
two hours their progress was rectilinear. The inclination of this 
part of the curve differed for each salt. I assumed that during 
the rectilinear period the rate of rise in concentration would be 
directly proportional to the velocity of diffusion of the salt. In 
order to test the validity of this assumption I made experiments 
with lithium, sodium and potassium chlorides, since the relative 
rates of diffusion of these substances have been determined already 
by physicists, using other methods:):. 

* A gelatine jelly of this strength has been shown by Hardy to have the struc- 
ture of an open network. 

t Quoted in Handhuch der anorg. Chemie, ii. 1, Abegg u. Auerbach, 1908. 
Also, Landolt-Bornstein's Tabellen, 1903. 

X I have unfortunately been unable to apply the method of calculation, since 
worked out by Mr Hill, to these observations owing to the neglect of a simple 
precaution in my first experiments. The solution was introduced at a temperature 


384 Mr Mines, On the relative velocities of diffusion in 




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go '5'^ 

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pq CQ 

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aqueous solution of rubidium and caesium chlorides. 385 

One experiment may be quoted at length. 

In this experiment there was a period of four hours, during 
which the increase in concentration proceeded at a practically 
uniform rate. 

At 5.30 the concentration was -00303 Mol. NaCl. 

At 9.30 „ „ „ -0087 „ „ 

Thus in four hours the increase was 'OObOll or •001417 per 

Experiments made in the same way with the other salts 
yielded the following numbers. The observations are plotted in 







/yy y^ 

























yy X 





lOorS ^ ' 






'7 V 'f^ /o 

Fig. 2. 

Deci-normal Caesium chloride.. 

„ Rubidium chloride 

„ Potassium chloride 

„ Sodium chloride .. 

„ Lithium chloride ... 

•0018 Mol. per hour 
•001748 „ „ „ 
•001707 „ „ „ 
•001417 „ „ „ 
•001165 „ „ „ 

Or taking the rate of diffusion of potassium chloride as unity, 
and disregarding the last decimal place, we have 

CsCl 1-05(5), RbCl 1-02(3), KCl 1-000, NaCl 0830, LiCl 0-68(4). 

below that of the water bath and some few minutes must have elapsed before 
18° was reached. The effect of this delay is to slightly displace the curve to the 
right without affecting its form except at the very beginning. My calculations are 
based entirely on the inclination of the curve during a period beginning three 
or four hours after the experiment was started. 

386 Mr Mines, On the relative velocities of diffusion, etc. 

In the following table these results are compared with some 
figures given by previous observers for the relative diffusivities of 
potassium, sodium and lithium chlorides. 









Beilstein*, 1856 






Schuhmeisterf, 1879 






Long+, 1879 






Oholm§, 1905 






J. C. Graham II, 1905 






J. C. Graham 11,1907 






Mines, 1910 

It will be noticed that in the last two columns my numbers 
fall within the limits of variation of those quoted above. This 
fact I consider to justify the extension of the method to the study 
of rubidium and caesium chlorides. In making these experiments 
I aimed only at getting a rough comparison of the diffusion rates 
of these substances, but I believe that the method might be used 
to obtain values of considerable accuracy. 

It would be easy to simplify the conditions by keeping one 
end of the cylinder of jelly in contact with a dilute salt solution 
renewed at frequent intervals and the other end in contact with 
distilled water. It is obvious that the method is limited to those 
electrolytes which are not hydrolysed in solution. 

Conclusion. In dilute aqueous solution at 18° C rubidium 
chloride diffuses slightly faster than potassium chloride and 
caesium chloride slightly faster than rubidium chloride. 

The chlorides of the alkali metals show a rise in their rate of 
diffusion which follows the same order as the increase in their 
molecular weight and in the velocity of their kations. 

My f]-iend, Mr A. V. Hill, of Trinity College, has kindly indi- 
cated a mathematical treatment of the subject in the following 

* Beilstein, Liebig's Annalen, xcix. 1856, p. 165. 
+ Schuhmeister, Landolt-Bornstein's Tabellen, 1905. 
X Long, Annalen der Physik u. Chemie, ix. 1880, p. 613. 
§ Oholm, Zeit. Physik. Chem. l. 1905, p. 309. 
II J. C. Graham, ibid. p. 257. 
II Ibid. Lix. 1907, p. 691. 

Mr Hill, Use of experimental method of preceding paper. 387 

Note on the use of the experimental method described in the 
preceding paper. By A. V. Hill, Scholar of Trinity College, and 
George Henry Lewes Student. 

AGDB is the tube containing the gelatine, which stretches 
from AB to the bottom CD of the tube. Then the conditions 
throughout the gelatine ACDB must be the same as if we had 
double as much gelatine AEFB, and KCl (e.g.) solution at each 
end. For in the first case the bottom of the tube hinders diffu- 
sion across the plane AB: in the second case from considerations 
of symmetry there can be no diffusion across the plane CD. 

Gg and Hh are the platinum electrodes. AG = -^= CE. 

Let y be the concentration at any point P measured a distance 
X along the tube. 

Then we have the equation for the diffusion, 

dt dx" 
if t is the time. 

A solution of this equation which satisfies all conditions is 

r=oa _j^] 

y^yo+ 2 Are 

■ f . rirx 

sm , 


For (1) at ^ = 0, y = yo, the constant concentration of KCl. 

(2) at « = a, 2/ = 2/o- 

(3) y can be made equal to at ^ = 0. 
We have at ^ = 

i) = yQ + ZAr sm ■ . 

1 <^ 

388 Mr Hill, Note on the use of the experimental 

Multiplying h} 
and a, we have 


Multiplying by sin , and integrating between the limits 


f ^ TlTCC f ^ 

= 2/0 sin --— + ^ J 

.0 «. Jo 

. „ rirx 




rira ^ 

cos cos 


A ^^ 

when r is even .4,. = 0, 

when r is odd J.,. = . — Vo • 2 = — ~ , 

a rir'-^ rir 

y = 2/0 i 1 - 4 S r^ ^^— e «- sm ^ — \ . 

"^ "^ ( 1 (2n-l)7r a j 

Hence we may draw two conclusions. 

(1) To make results with the instrument easily and 
directly comparable it is advisable to keep ^ , the amount of 
gelatine used, the same in different experiments. 

(2) With this condition if kt in one experiment =k't' in 
another, the concentration at any point P is the same in either 
experiment. Hence if we compare the times at which equal 
concentrations are reached these must be inversely proportional 
to the diffusion constants of the two salts. With a series of 
observations therefore at equal intervals of time the concentrations 
can be plotted and the curve compared with the standard curve 
obtained for one salt whose diffusion constant is known. The 
ratio of the times to equal concentrations can be compared at 
several points of the curve : this ratio should be found nearly 
constant, and its mean value for several concentrations will give 
the ratio of the diffusion constants very accurately. 

If we suppose the conductivity to be directly proportional to 
the amount of salt between the two electrodes we shall have the 

A P (i A.K 1 -k^^^t . (2n-l)'7rx\. 

^ = f^yo i 1 - 4 2 ^ =^ e « sin -^ } dx, 

^^Jp\ i(2w-l)7r a ] ' 

where p and q are the values of x for the ends g, h, and G, H, of 
the electrodes, and jjl is some constant, depending on the conduc- 
tivity and the size of the plates. 

^ 1 {zn — lfir^ [ a 

(2n — 1) 7rq\ 

A = /x2/o 

— cos- 

method described in the preceding paper. 389 

From a measurement of the constants a direct estimation 
might be made of the diffusion constant of any one salt. 

By plotting the logarithms of the time and the logarithms of 
the conductivities the curves for two different salts will be found 
to be the same, though situated at a different position. The 
amount that one must be displaced along the axis of time in 
order to coincide with the other gives the ratio of the diffusion 
constants : the amount of displacement along the axis of con- 
ductivity gives the ratio of the conductivities. 


il/r- Arber, A note on some fossil 

A note on some fossil plants from Newfoundland. By E. A. 
Newell Arber, MA., F.L.S., F.G.S., Trinity College. 

[Read 7 February 1910.] 

The present preliminary note is concerned with two fossil 
plants, not hitherto recorded from Newfoundland. Our know- 
ledge of the plant-remains from this region is at present very 
slight, and is confined to a few Upper Carboniferous species de- 
scribed by Dawson*. The impressions, discussed here, occur in 
a sandy shale exposed in the bed of the Shenanditti River, on 
the west side of Red Indian Lake in the interior of Newfoundland. 

Text-fig. 1. Sphenophyllum tenerrimum, Stur. 

Two leaf whorls, each composed of six or more repeatedly dichotomous, narrow 
segments. No. 269 Sedgwick Museum, Camb. x 2. 

The specimens, which are well preserved, were presented to the 
Sedgwick Museum by the generosity of Mr Rowland Feilding in 

There are only two species to be recorded and these were 
associated. One of them is a Sphenophyllum, which appears to 

* Dawson, Rep. Foss. Plants, Loiver Carbon, and Millstone Grit, Canada (Geol. 
Surv. Canada, 1873), pp. 29, 32, 34. 

plants from Neivfoundland. 391 

be very closely similar to, if not identical with, Sphenophyllum 
tenerrimum, Stur*, known from the Lower Carboniferous rocks of 
Silesia. Both leaf whorls and stem impressions are represented. 
Two of the former are seen in text-fig. 1, magnified twice. 

The whorl consists of six or more dichotomously branched 
narrow segments. In some cases the leaves dichotomise twice, 
in others, three times. The first dichotomy may take place at 
the base of the leaf, or a little above the base. 

Sphenophylls possessing this reduced and repeatedly forked 
type of foliage are known both from the Lower and Upper 
Carboniferous. In some Coal measure species, both normal wedge- 
shaped leaves and leaves with reduced forked segments may 
occur on the same stem. In the case of S. tenerrimum, Stur, 
however, as in the present specimen, there are no indications 
that would lead one to suppose that the plant was heterophyllous. 

With the Newfoundland specimens we may also compare the 
Sphenophyllum subtenerrimum of Nathorst-f* from the Upper 
Devonian rocks of Bear Island in the Arctic regions. Here how- 
ever the leaf whorls appear to be smaller in size|, and the leaf 
segments even more delicate. 

Impressions of stems of Sphenophyllum, possibly belonging to 
the same species as the leaves described above, are also associated. 
One of these is shown in text-fig. 2, where two somewhat tumid 
nodes are seen, with which fragments of leaves, which lie at right 
angles to the plane of the stem as seen in this specimen, appear 
to be still in continuity. The internodes exhibit two rather 
sharp longitudinal ridges, which are fairly distant from one 

This stem appears to be somewhat stouter, and the internodes 
more elongated, than the stem specimens of S. subtenerrimum, 
figured by Nathorst. 

The other plant collected from the Shenanditti River is of 
special interest for it appears to be new to science, at least 
specifically, if not generically. In Mr Feilding's collection, several 
examples of a large fan-shaped leaf are more or less completely 
preserved. These leaves often exceed 14 cm. in length and 
breadth. The nerves radiate from the base and are numerous, 
dichotomising here and there in the broader portion of the leaf. 
All the examples are detached. At the base the leaf narrows 
somewhat rapidly and appears to have been sessile. 

These leaves recall some species of the rare and little known 
genus Psygmophyllum, Schimper, more closely than any of the 

* Stur (Culm Flora, Part ii.), Ahhandl. k. k. Geol. Reichsanst, Wien, Vol. viii. 
1877, p. 108, pi. VII. (xxiv.), figs. 1—14. 

t Nathorst, K. Svenska Vetenskaps-Akad. Handl., Yol. xxxvi. No. 3, 1902, p. 23, 
pi. 2 (figs. 14—17), pi. 3 (figs. 7, 8), pi. 4 (figs. 14—23), pi. 5 (fig. 5). 

X Ibid., pi. 4 (figs. 22, 23). 

392 Mr Arher, A note on some fossil plants, etc. 

other fossils recorded from the Palaeozoic rocks. Psygmophyllum 
as at present constituted is probably a composite genus. At a 
future opportunity it is proposed, when describing these fossils 
more fully, to review the present position of our knowledge of 
the plants which have at one time or another been assigned to 
it. The present preliminary note may serve to record the dis- 
covery of these interesting fossils in a region which hitherto has 
remained almost a terra incognita in a palaeobotanical sense. 

Text-fig. 2. Sphenophyllum, sp. 

A stem showing two nodes, to which fragments of leaves are attached. 

No. 339 Sedgwick Museum, Camb. x 1|. 

The only evidence of the age of the rocks from which these 
specimens were obtained is that presented by the fossils them- 
selves. From the occurrence of Sphenophyllum tenerrimum, 
Stur, one would suppose that the period is either Lower Carboni- 
ferous or Upper Devonian, the former being more probable. 

Mrs Arber, A note on Cardiocarpon compressum, Will. 393 

A note on Cardiocarpon compressum, Will. By Mrs E. A. 
Newell Arber, D.Sc, Newnham College. (Communicated by 
Mr E. A. Newell Arber.) 

[Head 7 February 1910.] 

In 1877 Williamson* described and figured a small unattached 
winged seed showing binary symmetry, from the Lower Coal 
Measure nodules of Oldham, which he referred to Brongniart'sf 
genus Cardiocarpon. On account of its flattened form he gave it 
the specific name compressum. Other Cardiocarpons had previously 
been described from the British Coal Measures, but only their 
external appearance was known, whereas in the new species the 
internal structure was preserved. Williamson figured sections cut 
from three specimens. The most characteristic feature of the seed 
was that the testa was divisible into two very distinct layers, — 
an exotesta of coarse parenchyma, and an endotesta of much 
smaller cells. No further description of the internal structure of 
Cardiocarpon compressum, or of that of any other seed showing 
bilateral symmetry from the British palaeozoic rocks, has been 
published since Williamson's time. The main interest of the 
genus Cardiocarpon lies in the great probability that it repre- 
sents the seeds of Cordaites^. The possibility is not however 
excluded, that seeds of this type were borne by Pteridosperms, 
for seeds of binary symmetry have been found attached to fronds 
of Aneimites^ and Pecopteris Pluckeneti\\. The following note 
is based on material collected by Prof. F. W. Oliver, Dr D. H. 
Scott, and Prof. Weiss, and generously made over to the present 
writer for examination. The material consists entirely of sections 
of unattached seeds occurring in the " coal balls." The same 
seed is seldom met with in more than one section. 

The contrast between exotesta and endotesta already men- 
tioned afibrds the readiest means of identifying Cardiocarpon 
compressum in microscopic section. There is sufficient variation 
among the specimens, both in dimensions and structure, to suggest 
that Cardiocarpon compressum, instead of being a single species, 
may possibly represent an assemblage of seeds belonging to closely 

* W. C. Williamson, " On the Organisation of the Fossil Plants of the Coal- 
measures," Pt. VIII., Phil. Trans. Boy. Soc. Vol. clxvii. Pt. i. p. 213. 

t A. Brongniart, Prodrome d\me histoire des vegetaux fossiles, Paris, 1828. 

X F. C. Grand'-Bury, Memoire sur la Flore Carbonifere du Departement de la 
Loire, 1877, p. 233. 

§ David White, "The Seeds of Aneimites," Smithsonian Miscellaneous Collec- 
tion, Vol. XLVii. 1905, p. 822. 

II F. C. Grand'-Eury, " Sur les graines trouvees attachees au Pecopteris Plucke- 
neti, Schlot," Comptes Rendus, t. cxl. 1905, p. 920. 

394 Mrs Arber, A note on Cardiocarpon compressum, Will. 

allied plants. The sclerotesta or shell consisted of two flattened 
valves, pointed above and broadest near the base. In both length 
and breadth these valves slightly exceeded half a centimetre. 
In well preserved specimens the shell is enclosed in a delicate 
sarcotesta forming a thin layer over the surface of the valves, 
and at their lateral edges extending beyond them as a wing 
lying in the plane of flattening. The wing appears to have 
terminated in a short downward prolongation on each side of 
the hilum, giving the seed a remote resemblance to a mitre. It 
should be mentioned that Williamson took a different view of 
the structure, and figures the sarcotesta as continuous round the 
base of the seed. 

Williamson's preparations did not admit of his observing the 
vascular system, which is of some interest. The main supply 
bundle enters the hilum and expands into a funnel-shaped mass 
below the nucellus. Here it gives off two opposite branches in 
the plane of flattening of the seed. These branches are at first 
horizontal, but they soon bend downwards and outwards, travers- 
ing the shell in an oblique direction. On emerging into the 
sarcotesta they curve upwards and run to the micropyle following 
the slight groove at the junction of the valves. The base of the 
nucellus is supplied by tracheides given off from the expanded 
end of the central bundle above its two main branches. I have 
not been able definitely to satisfy myself as to whether a nucellar 
vascular system arises from this basal tracheal plate. 

Inside the shell there are indications of an "inner flesh," 
which is however seldom preserved. The nucellus seems to have 
been free from the integument from the base upwards. The 
megaspore is usually empty and contracted, but in one case a 
tissue occurs within it which may be a prothallus. 

I have provisionally adopted Williamson's name for this seed, 
Cardiocarpon compressum, but it is doubtful whether it should 
be permanently retained. The question of nomenclature, which 
presents some difficulties in this case, will be discussed at length 
in a detailed paper which I hope to publish shortly. 

Mr Gordon, On a new species of Physostoma, etc. 395 

On a new species of Physostoma from the Lower Carboniferous 
Rocks of Pettycur (Fife). By W. T. Gordon, M.A., B.Sc, Falconer 
Fellow of Edinburgh University, and Advanced Student Exhibi- 
tioner of Emmanuel College. (Communicated by Mr E. A. Newell 

[Bead 7 Tebruary 1910.] 

Among the rarer petrifactions of plant-remains occurring in 
the Calciferous Sandstone Rocks at Pettycur are seed-like bodies 
of various kinds. Perhaps the commonest example is Lepido- 
carpon wildianuni, Scott*, while occasionally the pteridospermous 
fructification — Gonostoma ovale, Williamson "f*, is also met with. 
Under the name Conostoma interinediaX Williamson also placed 
what are probably elongated specimens of G. ovale. These two 
seed bodies are very distinct, for Gonostoma has a funnel-like 
micropyle, whereas Lepidocarpon has no true micropyle. The 
megaspore in the latter was exposed to the exterior by means 
of a slit-like aperture between two enveloping outgrowths from 
the sporophyll. 

Last year Prof. 01iver§ published his work on Physostoma 
elegans, and showed that in that genus the apex of the seed 
consisted of closely adpressed, free, tentacular processes; the 
micropyle was thus capable of great enlargement. 

In the same paper he refers to C. ovale as being probably the 
seed of Heterangium grievii, Williamson. The only evidence 
however is association. Recently, while examining a new species 
of Heterangium from Pettycur, I discovered several specimens of 
C. ovale, and among them what appears to be a new and distinct 
seed. The specimen had been cut through in an oblique tan- 
gential direction, but by careful preparation I was able to get 
one of the sections more nearly radial. One section is through 
the micropylar orifice and the other passes through the chalaza. 

General Structure. 

The seed is radially symmetrical and is considerably larger 
than G. ovale. The following table gives the dimensions of the 
new seed and those of G. ovale. 

* Scott, Phil. Trans. Roy. Soc. B. Vol. cxciv. 1901, p. 291, 

t Williamson, Ibid. Vol. clxvii. 1877, p. 243. J Ibid. p. 246. 

§ Oliver, Ann. Bot. Vol. xxin. 1909, p. 73. 

896 Mr Gordon, On a new species of Physostoma 

New Seed {Physostoma) 

Conostoma ovale 



3-8 mm. 
3'3 mm. 

3-2 mm. 
2"1 mm. 

Average of 
5 radial 

The length of the new seed is probably greater than indicated, 
since both sections are oblique, and 4 mm. would probably not 
be an excessive estimate of the true length. The breadth is also 
considerable, and indeed the almost globular shape of the seed 
is striking. The base is rather flat and the micropyle is not 

The seed at the apex shows a number of tentacular processes 
and the outer surface is studded with small peg-like hairs. The 
occurrence of these characters warrants its inclusion in the genus 
Physostoma as lately defined by Oliver. 

All the Pettycur seeds I have examined are poorly petrified, 
and this new one is no exception. The description must there- 
fore be meagre. 

The nucellus is capped by the pollen chamber but there is 
no dome-like projection of the nucellar apex into the cavity of 
the pollen chamber. Indeed, in that region the seed is quite like 
Conostoma and not Physostoma. Outside the membrane of the 
nucellus the tissues are all decayed; only the vascular bundles 
remain. Near the chalaza however and in one of the apical 
processes a slight amount of delicate parenchymatous tissue 
can be observed, but it is too fragmentary to warrant detailed 

The outer layers of the integument have all decayed into a 
structureless dark zone about "2 mm. thick. There are no ribs 
on the outside of the seed, but the whole periphery is covered 
with small dark dots. These lie in a zone concentric with the 
seed and about "l mm. outside. Near the micropyle these dots 
are seen to occupy the ends of short finger-like cells which clothe 
the seed externally. They are quite similar to the peg-cells of 
Lagenostoma and may be equivalent to the hairs on Physostoma 
elegans. In this new specimen the hairs are equal in length all 
over the surface. In outline the hairs are short and have rounded 

The most interesting part of the seed, however, is the raicro- 
pylar end. There we find a pollen chamber in the usual position 
at the apex of the nucellus. The orifice of this chamber is not 
visible owing to the obliquity of the section and it is uncertain 
whether there was a funnel-shaped aperture as in Physostoma 

from the Lower Carboniferous Rocks of Pettycur (Fife). 397 

elegans or a depressed aperture as in Conostoma ovale. The 
micropyle which lies immediately over the opening of the pollen 
chamber is also cut tangentially and in the most radial section 
is clearly bounded by three separate tentacle-like processes. 

The chalazal end is also interesting from the fact that the 
bundles enter the seed independently as in Physostoma. 

This new species of Physostoma, which is more ancient than 
P. elegans recently described by Professor Oliver, combines 
with its Physostoma characters, others which are typical of the 
genus Lagenostoma. The tentacular processes at the apex 
suggest affinities with Lagenostoma in that they are less di- 
vergent than in Physostoma (i.e. they clasp the pollen chamber 
more tightly), and thus the seed has the whole apex flattened 
as in Lagenostoma. On the other hand the structure of the 
pollen chamber, so far as is known, is quite unlike that of 
Lagenostoma. The seed may however eventually require to be 
placed in a new genus. 

In conclusion I have to thank my supervisor Mr Arber for 
his kindly criticism and advice. 

VOL, XV. PT. V. 


398 Mr Gordon, On the relation between the 

On the relation between the fossil Osmundaceae and the 
Zygopterideae. By W. T. Gordon, M.A., B.Sc. (Edin.), Falconer 
Fellow of Edinburgh University, and Advanced Student Exhi- 
bitioner of Emmanuel College. (Communicated by Mr E. A. 
Newell Arber.) 

[Read 7 February 1910.] 

The structure of the axis in the living Osmundaceae has given 
rise to two main contentions as to the evolutionary position of the 
group. The axis is regarded by Jeffrey* and Faullf as reduced 
from a more complex dictyostelic ancestor, and by Boodle j, Seward 
and Ford|, Chandler ||, TansleyH, and Kidston and Gwynne- 
Vaughan** as the latest development in an ascending series from 
a protostelic ancestor. 

This latter view is supported by the ontogenetic development 
of living species and, now that Kidston and Gwynne-Vaughan 
have completed their studies on the fossil representatives, by the 
phyllogeny of the group as well. 

The present living genera may be placed in two categories. 
Osmunda regalis may be taken as one extreme type where the 
leaf gaps are long and a cross-section of the stem consequently 
showing a ring of several xylem strands. In cases where the 
leaf gap is short as in Todea barbara and T. superba a cross-section 
shows the xylem as a much more continuous ring. This may be 
looked upon as the other extreme. 

The stems of the most recent fossil representatives of the 
Osmundaceae conform to these two extremes. Even Osmimdites 
Skidegatensis, Penhallow, is of the Osmunda regalis type, though 
it may be regarded as an even more extreme example. (This 
species seems to lend colour to Jeffrey's reduction theory, but 
the weight of the other evidence completely overrules this 
single exception.) The tertiary species Osmundites schemnicensis 
(Pettko) and 0. Dowkeri, Carruthers, resemble Osmunda regalis, 
and so does the Jurassic form 0. Gibbiana, Kidston and Gwynne- 
Vaughan. 0. Dunlopi, Kidston and Gwynne-Vaughan, another 
species from the Jurassic, has a xylem ring which is almost later- 

* Jeffrey, Pliil. Trans. Roy. Soc. Vol. cxcv. 1902, p. 127. 

+ Faull, Bot. Gaz. Vol. xxxii. 1901, p. 418. 

t Boodle, Ann. Bot. Vol. xvii. 1903, p. 515. 

§ Seward and Ford, Trans. Linn. Soc. London, Series 2, Vol. vi. 1902, p. 254. 

II Chandler, Ibid. Vol. xix. 1905, p. 406. 

U Tansley, New Phytologist, Eeprint No. 2, 1908. 

** Kidston and Gwynne-Vaughan, Trans. Roy. Soc. Edinburgh, Vol. xlv. Pt. 3, 
1907, p. 759; ibid. Vol. xlvi. Pt. 2, 1908, p. 213: ibid. Vol, xlvi. Pt. 3, 1909, 
p. 651. 

fossil Osmundaceae and the Zygopterideae. 399 

ally continuous, i.e. the leaf trace departs typically in a protostelic 
manner. This also occurs occasionally in T. superba, so that 
0. Dujdopi may be considered as pointing to Todea rather than 
to Osmunda regalis. 

In the Jurassic period therefore forms existed which were 
practically as divergent as the living ones are. The only differ- 
ence is shown in 0. Dunlopi, where the leaf trace is typically 
protostelic in its departure. The type of this last species is 
still further accentuated in Upper Permian times in the case 
of Zalesshya, Eichwald, and Thamnopteris, Eichwald. Both of the 
last-named genera have not only the xylem ring continuous 
laterally but they have no central pith. The central tissue of 
the stem consists of short, reticulated tracheides. 

In the Permo-Carboniferous genus Grammatopteris Kidston 
and Gwynne-Vaughan see the earliest example of a plant with 
Osmundaceous affinities, and here we find a perfect protostele 
with only one type of xylem tissue. This genus however is still 
imperfectly known. 

The leaf trace in the fossil Osmundaceae also shows a very 
distinct passage from exarchy to endarchy, and from protostelic 
departure to cases where leaf gaps occur. The most interesting 
example is probably Thamnopteris schlechtendalii, since in it we 
occasionally find leaf traces with double mesarch protoxylem 
groups. Even where such double protoxylems are found the 
trace develops normally afterwards. 

Turning now to Zygopterid alliance, we find that the youngest 
known representative is Asterochloena Corda ranging to the 
Devonian. The stem xylem in this genus is stellate with exceed- 
ingly long rays and a pith is always present. The trace has two 
mesarch protoxylem groups. In the Permo-Carboniferous of Autun 
Z. Brongniarti, Renault, occurs. The stele in this case has almost 
circular xylem with a true pith and a system of internal tracheides 
in that pith. The outer xylem ring is interrupted by the depart- 
ing leaf traces. Z. Grayi, Williamson, from the Coal Measures, has 
a stellate xylem but the rays are very short. A central pith and 
system of internal tracheides are present. 

Corresponding to Z. Brongniarti in the Permo-Carboniferous we 
have Z. Corrugata, Williamson, in the Coal Measures. The organisa- 
tion of this stem is quite similar to Z. Grayi, but in outline it has 
become more circular. The differences between the outlines in 
these two species seems to be correlated with the greater length of 
the internodes. The lately discovered stem of Diplolabio Romeri 
Solms from Lower Carboniferous rocks exhibits the most primitive 
type of zygopterid stem so far known. The stem as seen in trans- 
verse section, in cases where no petioles are departing would be 
classed as a Botryopterid. The wood is solid and of two kinds, 


400 Mi^ Gordon, On the relation between the fossil, etc. 

forming an inner and an outer zone. The thickenings on all the 
elements are reticulate, except the protoxylem groups, where they 
are scalariform. The leaf trace departs in a protostelic manner, 
and has two immersed protoxylem groups. 

Among the Botryopterideae, B. cylindrica (Williamson), from 
the Coal Measures, represents probably the highest known type 
of development. Here the inner elements of the stem xylem 
are smaller than those of the outer xylem. In B. antiqua, 
Kidston, there is only one type of xylem element. In the last 
species I have been able to show that the leaf trace is at first 

The thickenings on the xylem elements in these three groups 
are interesting. In the Osmundaceae we get a series from 
multiseriate pits through scalariform to reticulate thickenings. 
Reticulate tracheides only occur in the archaic forms Zalesskya 
and Thamnopteris and then only in the inner wood. The last- 
mentioned type of thickening must therefore be considered the 
most primitive. Among the Zygopterideae we find a similar 
series from scalariform to reticulate (in D. Romeri) ; in the 
Botryopterideae from scalariform to reticulate. 

Except for the multiseriate pits on the external xylem elements 
Thamnopteris could not be distinguished from the zygopterid 
D. Romeri on stem structure. The leaf trace has of course typi- 
cally only one protoxylem group, but occasionally examples with 
two are found. This feature may be considered as being probably 
primitive since the double group ultimately functions as if it 
were a single one. In D. Romeri the leaf trace has typically two 
protoxylems and I have never observed either more or fewer than 
that number. It is clear then that at first sight in their most 
primitive representatives the two groups of the Osmundaceae and 
the Zygopterideae cannot be distinguished in their anatomical 
features. The two groups show exactly parallel development 
from the two primitive types just cited, and it thus seems prob- 
able that they have diverged from a common stock. The 
geological position of the various representatives of these groups 
points to the conclusion that the Zygopterideae diverged from 
the parent stock before the Osmundaceae did; and the greater 
suitability of the latter group for present conditions of growth 
has allowed it to persist after the Zygopterideae had perished. 

I desire to express my indebtedness to Mr E. A. Newell Arber, 
under whose supervision my work is being carried on, for his 
criticism and advice. 

if?' Vernon, On the occurrence of Schizoneura paradoxa, etc. 401 

On the occurrence of Schizoneura paradocca, Schimper and 
Mougeot, in the Bunter of Nottingham. By R. D. Vernon, 
B.Sc, 1851 Exhibition Research Scholar, and Advanced Student 
Exhibitioner of Emmanuel College. (Communicated by Mr E. A. 
Newell Arber.) 

[Read 7 February 1910.] 

From the Eugiish Trias recorded fossils are extremely rare and 
appear to be restricted to the Upper or Keuper division. The 
Lower Trias has hitherto yielded, so far as I am aware, only 
derived fossils which are contained in the constituent pebbles of 
the middle or " Pebble Bed " subdivision of the Bunter. The 
discovery of fossil plant-remains from the Bunter of Nottingham 
is thus of some general interest, for they appear to be the first 
contemporaneous fossils from the Bunter of England. Equise- 
taceous pith casts of doubtful attribution were the first specimens 
obtained ; they were provisionally determined as Equisetites sp., 
and are so mentioned in the recently published Geological Survey 
Memoir on the Nottingham district*. Subsequent collecting has 
yielded a large number of fragmentary plant-remains including 
not only pith casts but also leaves, stems, and roots ; occasionally 
specimens are found showing two or more organs still in organic 
connection. All the fossils may be referred to Schizoneura para- 
doxa, S. and M., and there is reason to believe that they originally 
grew on the spot where they now occur. 

The fossiliferous section is a now disused sand-pit at the foot 
of Colwick Wood, by the west side of the Great Northern Rail- 
way bridge ovei- Colwick Road, Nottingham. The section shows 
the regularly-bedded marls and thick sandstones of the Lower 
Keuper (Waterstones) with a thin conglomerate at the base, 
resting on a sharply marked and eroded surface of the Bunter 
Pebble Beds, which here consist of strongly current-bedded pebbly 
sandstones containing nodules and lenticular beds of red marl. 
It is from the uppermost lenticular bed of marl in the Bunter, 
a few feet below the basal conglomerate of the Keuper, that 
all the plants have been collected. The section is figured and 
described at length in the Geological Survey Memoir on the 
district •!-. 

* " Geol. country between Newark and Nottingham" (Mem. Geol. Sui-v.), 1908, 
p. 42. 

t Ibid. p. 37. 

402 Mr Vernon, On the occurrence of Schizoneura paradoxa, 

Schizoneura paradoxa, Scbimper and Mougeot, 1844. 

1828, Calamites arenaceus, Brongniart, Hist, veget. foss. PI. xxiii. 

fig. 1. 
1844. Schizoneura paradoxa, Schimper and Mougeot, Monog. 

Plant, foss. Vosges, p. 48, Pis. xiv. xv. xvi. 
1844. Calamites arenaceus, ibid. p. 57, PI. xxviii. fig. 2. 
1844. Catamites mougeoti, ibid. p. 58, PL xxix. figs. 1, 2, 3. 
1870. Equisetites mougeoti, Schimper, Traite, p. 279, PI. xii. 

1907. Equisetites arenaceus, Arber in Wills' Geol. Mag. Dec. 5, 

Vol. IV. p. 32. 
1910. Schizoneura paradoxa, Wills, Proc. Geol. Assoc. Vol. xxi. 

Part 5, p. 272. 

Localities. Voltziensandstein (Upper Bunter) of the Vosges. 
Lettenkohle (top of Muschelkalk) at Neuewelt, Basle, Switzerland. 
Lower Keuper Sandstone at Bromsgrove and other places in 
Worcestershire. Bunter Pebble Beds of Nottingham. 

Diagnosis. From a study of tbe specimens in the Strassburg 
Museum, including the original material of Schimper and Mougeot, 
and of the Worcestershire specimens, described in his recent 
paper. Wills* has drawn up the following diagnosis: 

" Large plants, stems up to two inches in diameter, stems 
divided into nodes and internodes, internodes long, larger stems 
either ridged or smooth, pith either wholly or partially hollow; 
branches borne in whorls at the nodes, external surface of branches 
usually smooth or nearly smooth ; leaves long and strap-like, 
borne in whorls at the nodes, leaves united either into a sheath 
or into sheath segments or free to their bases, border of leaves 
smooth, median part of leaves with fine close-set parallel nerves, 
cone probably with peltate areas on external surface, roots arising 
from the nodes, roots small and repeatedly branched." 

Schizoneura must still be regarded as an imperfectly defined 
genus. Of the cone our knowledge is of the slightest, and of the 
internal anatomy of the plant we are quite ignorant. The frag- 
mentary nature of the stem casts renders identification in many 
cases doubtful or even impossible. Ridged and grooved casts are 
of common occurrence, some of these may represent the external 
surface of the stem, or they may be the impressions of the external 
surface more or less modified by the internal structure, as pointed 
out by Wills; more usually they are interpreted as pith casts. 
Such fragmentary pith casts cannot be generically identified, 
they may belong to one of several members of the Equisetaceae. 

* Wills, " The Fossiliferous Lower Keuper Eocks of Worcestershire," Proc. 
Geol. Assoc. Vol. xxi. 1910, Pt. 5, p. 272. 

Sohimper and Mougeot, in the Bunter of Nottingham. 403 

A further source of possible error depends on the fact that 
this diagnosis is necessarily founded on fragmentary material 
from various localities occurring in association with remains of 
other plants. This latter objection does not apply to the fossils 
described below since they appear to belong wholly to one species 
and are not associated with any other plant-remains. 

Description of the Specimens. 

Detached leaves. These are fragments of long, narrow, deli- 
cate, grass-like leaves, usually found detached but more rarely 
occurring in organic connection with a stem. They have smooth 
entire margins with a median group of exceedingly fine parallel 

One example has four and another has six leaves, in each case 
the margins of the leaves are arranged parallel to one another. 
These specimens may be regarded as portions of sheath-segments 
composed of several leaves, originally united by their smooth 
margins along the commissural lines. By splitting along these 
lines the leaves have, in some cases, become either partially or 
wholly free. 

Leafy shoot. A cast of the external surface of a small stem 
about "5 cm. in diameter with a smooth, irregularly wrinkled 
surface, bears a node from which arise four or more leaves forming 
a leaf-sheath. Only the basal portions of the leaves are preserved, 
and the clasping nature of the leaf-sheath cannot be made out 
because the specimen has been flattened by crushing. 

Leafless stems. The material furnishes at least four kinds of 
casts and impressions of leafless stems : 

(a) The first type are characterised by a smooth, irregularly 
wrinkled surface and distinctly swollen nodes. 

In these features they agree exactly with casts of the external 
surface of leaf-bearing stems. 

(h) Occasionally a cast of the above type is folded into some- 
what broad furrows and narrow ridges. 

A similar structure occurring in casts of Schizoneura meriani 
was explained by Schimper * as due to an accident of preservation. 

(c) Several casts of portions of large stems differ from type 
(<x) only in the fact that their smooth surfaces are faintly but 
regularly ridged and grooved. They may be regarded as either 
the casts of the external surface of large, faintly-ribbed stems, 
or the ribbing may be ascribed to the action of the internal 

{d) What appears to be a more internal cast than the above 
has internodes strongly marked with longitudinal ridges and 

* Schimper, Traite de Palaeontologie Vegetale, 1869, p. 282. 

404 Mr Vernon, On the occurrence of Sckizoneura pa^^adoxa, 

grooves, which, in the best preserved specimens, appear to be 
continuous at the node. The specimens vary greatly in size, in 
the coarseness and fineness of the ribbing, and in the character 
of the ribs, which are generally broad and nearly flat-topped. 
Reversed casts also occur in which the ridges are represented by 
grooves, causing the true grooves to stand out as narrow ridges, 
whilst the nodal constriction is now represented by an upstanding 
ridge. These specimens are undoubtedly Equisetaceous pith 
casts, which, by themselves, cannot be generically identified. 

Branching. Certain specimens of the {d) type appear to be 
casts of the pith cavity of large branches. They are gradually 
contracted towards the base of the branch, just as is the case 
with the medullary casts of Calamites. Large scars which occur 
on the nodes of other casts of the {d) type may thus be inter- 
preted as branch scars. 

Nodal Diaphragms. Some interesting examples of nodal 
diaphragms have been collected. One specimen of the exterior 
portion of a stem with a node shows a diaphragm displaced by 
crushing, somewhat in the manner so often found in Equisetites 
lateralis. Other specimens have a smooth, central concave portion, 
bearing at the node a number of long, stout, narrow, spoke-like 
structures which appear to be branches. 

Many of the diaphragms, apparently belonging to the under- 
ground stem, are still in the position of growth and appear to 
have suffered hardly any distortion. Radiating from the edge 
of the node are four, five, sometimes six, roots which at first 
are confined to one plane; they bear numerous branching 
rootlets which ramify in all directions. One specimen of a small 
diaphragm, only 12 mm. in diameter, has, attached to the node, 
four roots which bear numerous rootlets. Another broader, thicker, 
more woody looking structure with a smooth surface is also borne 
at the node ; this appendage is quite different from, and very 
much larger than the associated roots ; it appears to be a portion 
of a stem. 

Roots. In addition to the roots described above which are 
found still attached to the node, there are numerous examples 
of detached fragmentary roots and rootlets, which show the same 
characters. All possess a smooth, irregularly wrinkled, or finely 
reticulated, external surface. Occupying the central axis of the 
root in several specimens is a stout central structure which 
probably represents the stele, its surface bears the imprint of 
longitudinal and transverse lines giving an appearance strikingly 
suggestive of cell structure. 

The rootlets differ from the roots merely in size ; the angle 
they make with the root is sometimes 60° but usually 90°. 

Scliimper and Mougeot, in the Bunter of Nottingham. 405 


The fossils indicate a large plant with smooth stems at least 
three inches in diameter. Only the smaller stems appear to have 
borne leaves, which were at first united by their margins to form 
leaf segments or leaf sheaths. Later the leaves became more or 
less free to their bases by splitting along the commissural lines. 
The upper portion of the stem bore whorls of branches at the 
nodes, whilst the underground stem gave off numerous slender, 
probably adventitious, roots ending in branching rootlets. 

The vegetative organs of this plant are so similar to those of 
the Keuper specimens of Schizoneura paradoxa, S. and M., de- 
scribed by Wills, that they may be regarded as the same species. 

At the same time a few minor differences are noticeable. The 
pith casts differ amongst themselves, and also from the Keuper 
specimens, in size, and in the relative coarseness and fineness of 
the ribbing; such variations may be expected to occur even in 
different parts of the same plant. 

Whilst the Keuper specimens of the root usually make an 
angle of 60° with the rootlets, in the Bunter plant this angle is 
nearly always 90°. 

From the puckering of the leaves in the Keuper fossils Wills 
inferred that those organs were thick structures; but the leaves of 
the Bunter were undoubtedly thin and delicate. 

In conclusion it may be remarked that this discovery of the 
first evidence of contemporary life in the Bunter rocks of England 
is not merely an interesting fact. The occurrence of the same 
species of land plant in both the Lower Keuper and the Bunter 
is of importance as evidence that the unconformity between these 
two divisions of the Trias in the Midlands is probably not an in- 
dication of a long lapse of time. It further suggests that the 
physical conditions which prevailed during these two periods were 
not very diverse. 

406 Mr Wills, Notes on the genus Schizoneura, 

Notes on the genus 8chizoneura, Schimper and Mougeot. By 
L. J. Wills, M.A., F.G.S., Fellow of King's College. (Communi- 
cated by Mr E. A. Newell Arber.) 

[Bead 7 February 1910.] 

The genus Schizoneura though of widespread occurrence is 
still very imperfectly known. It was founded by the eminent 
French palaeobotanists, Schimper and Mougeot, in 1844*, on speci- 
mens from the Upper Bunter (Voltzien-sandstein) of the Vosges 
Mountains, which they described as S. paradoxa. Their definition 
is somewhat loose, but its essential points are that the plant is of 
an Equisetaceous nature, with stem divided into rather long 
internodes; the leaves which are borne in whorls at the nodes 
are at first united into a leaf-sheath. This later splits along 
commissural lines into sheath-segments or into individual leaves. 

Though various species have since been described from diffe- 
rent horizons and countries, little has been added to our knowledge 
of the structure of this plant since 1844. Recently I have had 
the good fortune to collect abundant material from the English 
Lower Keuper of Bromsgrove in Worcestershire, which in some 
ways supplements our knowledge of the species S. pai'adoxa. It 
may be of interest to point out some details of the nature and 
structure of Schizoneura as exemplified by this, the original, 
species. We may then be in a more advantageous position to 
answer the question, whether the name Schizoneura has been 
applied to plants genetically distinct or the reverse. 

I have, however, described the Bromsgrove material in some 
detail elsewhere f. Accordingly, I propose at present to mention 
only the chief points of interest displayed by this plant. ^ 

There is little doubt that S. paradoxa and possibly all the 
other species, were lovers of moist spots and, in fact, probably 
grew actually in the water; for we find at Bromsgrove rootlets 
and stems still apparently in their position of growth. A similar 
mode of occurrence has been noticed by other observers|. Schizo- 
neura paradoxa may well have reached a considerable height, for 
stems up to about 2" in diameter and several feet in length have 
been discovered. 

Leafy branches are the best known portions of this plant. 
The external surface of the smaller stems was probably smooth, 
while the larger ones may have been slightly ribbed. The leaves 
usually number seven. So far they have never been observed 

* Schimper and Mougeot, Monograjphie des Plantes fossiles du Gres bigarre de 
la chaine des Vosges, Leipzig, 1844. 

t Wills, L. J., Proc. Geol. Assoc. Vol. xxi. 1910, p. 271. 

J e.g. Kogers, A. W., and Seward, A. C. ; see Seward, Quart. Jourii. Geol. Soc, 
Vol. Lxiv. 1908, p. 89. 

Schimper and Mougeot. 407 

entirely united into a sheath, yet sheath-segments with vaiying 
numbers of leaves are found. On the other hand, the leaves are 
occasionally free to their bases. They are strap-like structures, 
with smooth margins and a bundle of fine parallel nerves down 
the centre. 

The stems from which the leaves had fallen previous to pre- 
servation are of various types. They are known from impressions 
and casts. The external surface may have been smooth or possibly 
finely ribbed. The internal casts or impressions are finely ribbed. 
There are, however, two types of these, and their interpretation 
must remain ambiguous until we learn something from petri- 
factions about the internal anatomy of these Mesozoic Equisetales. 
We may, nevertheless, note that the libbing appears to be coarser 
in the lower parts of the stem. 

On certain of the ribbed internal casts there are at the nodes 
two kinds of prints: — the larger lie just above the nodal line and 
are branch-scars, while the smaller ones probably represent leaf- 

The roots of 8. paradowa have been found, and closely resemble 
those of Calamites {Pinnularia). It is doubtful whether the fructi- 
fication has ever been discovered. 

The ribbed internal casts mentioned above sometimes encase 
an innermost cylindrical cast. This is smooth, and probably 
represents a cast of a partially hollow pith. Such a structure 
has not been noticed before, though I found exactly the same 
phenomenon in several examples of the so-called pith-cast of 
Eqidsetites mougeoti, Schimper and Mougeot, from the Bunter of 
the Vosges Mountains, which are preserved in the Strasburg 
Museum. This plant is there associated in the same beds with 
/S^. paradoxa. Though the smooth outer surface of E. mougeoti is 
known, examples with leaves have never been described. The 
pith-casts are indistinguishable from those of Schizoneura. Ac- 
cordingly it becomes ever clearer that E. mougeoti is merely the 
name given to large leafless stems of 8. paradoxa* . One point, 
however, is not evident : the smooth external cast seen in E. 
mougeoti has not, so far, been found at Bromsgrove. Yet the 
external surface of the smaller branches is smooth, and we may 
probably assume that the larger examples have still to be sought 

How far the presence of this innermost cast can be taken as a 
distinguishing mark of Schizoneura cannot be determined as yet, 
until it has been observed or disproved in other species. 

* In this connection it may be noted that Seward [loc. cit. p. 88) figures 
as Schizoneura, sp. a, a stem with smooth external surface enclosing a ribbed 
pith-cast, similar to both E. mougeoti and S. paradoxa, and calls attention to the 
resemblance of the whole fossil to the former. 

408 Mr Wills, Notes on the genus ScMzoneura, 

Having now examined what is known of the plant originally 
described as ScMzoneura, let lis turn to a consideration of the 
other species, with the special object of seeing whether the genus 
is homogenetic. 

Names have been given to seven species ranging in age from 
the Permo-Carboniferous to the Rhaetic, while several other 
fragments of stems have been referred to the genus. The follow- 
ing table gives the distribution in time and space and the chief 
characteristics of the various named species. 

One or two notes are necessary relative to the table. In 
the first place it will be observed that the description of the 
nervation of both S. africana and S. gondwanensis differs from 
the usually accepted one which states that stout median nerves 
are present. I have, however, examined undoubted specimens of 
S. gondwanensis at the South Kensington Museum, on some of 
which, e.g. No. V, 7099, several distinct fine parallel nerves can 
be seen. 

The original specimen also of S. africana (Asterophyllites of 
Hooker*) in the Museum of the Geological Society likewise shows 
some three distinct nerves down the centre of some of the leaves. 
I use the term leaf here, not as Seward has done in redescribing 
S. africana f, where he applies the word to what I would call a 
sheath-segment, but in the same sense as Schimper and Feist- 

In the second place, little is known of S. wardi, and the 
description given by Zeiller leaves some doubt as to its nature. 
It seems, however, possible that the nervation is multiple. 

Let us now refer to the table. It is evident at once that 
Halle is well justified in classing 8. carrerei, 8. hoerensis and 
8. meriani together, and the institution of the genus Neocalamites 
appears expedient. The type of plant represented by 8chizoneura 
(Neocalamites) carrerei seems to have been almost world-wide in 
distribution in Rhaetic times ; so far so, in fact, that the Euro- 
pean, Asiatic and African species are almost indistinguishable. 

Of the remaining species, 8. wardi, although but imperfectly 
known, appears to have approximated to the Neocalamites type : 
yet it may have possessed multiple nervation. In this case, as 
it is likely that the nervation is a generic quality, it could not 
be easily classed with that group but would fall in more naturally 
with the remaining species. 

These three, 8. paradoxa, 8. africana and *Si. gondwanensis, 
agree closely with one another in the possession of a multiple 
nervation, in the small number of leaves, and in the usual union 

* Bain, A. G., " On the Geology of Southern Africa," Trans. Geol. Soc. Ser. 2, 
Vol. vii. 1845-56 (1852), p. 175. 
t Seward, A. C., loc. cit. p. 89. 

ScMmper and Mougeot. 






Tonkin and probably 
S. Africa 

Sweden and Europe 

Central Europe 

Alsace and England 

Eoggeveld (Fish E.), 
S. Africa 



New South Wales 






Lettenkohle and Lower 
part of Keuper ? 

Bunter and Lower 

Beaufort Series (Per- 

Karharbari Beds 
(Lower Gondwana 

Upper and Lower 
Gondwana Series 

Upper Productive Goal 

Karoo Beds? 




Saidtobeuninerved. Traces 
of fine, very close-set, 
parallel nerves in one 

Several fine parallel nerves 
aggregated into the 
middle of leaf 

At least three fine parallel 
nerves down the centre 
of each leaf 

Surface of leaf is uniformly 
striated lengthwise by 
very fine and close lines 
which in the median re- 
gion become better defined 
and constitute a more or 
less distinct median nerve 

Three, or possibly more, 
distinct fine parallel 
nerves down centre of 


Many, long, probably al- 
ways free to their bases 

Fewer than in Nos. 6 and 7 

Few, broad, united at first 
into sheaths and later into 
sheath-segments, some- 
times free 

Fairly broad, about 30 in 
number. United into 
several sheath-segments 

About 27 narrow leaves; 
doubtfully united into 

Number 10-22. Broadish, 
usually united into ovate 
sheath- segments. When 
only two sheath-segments 
are present they simulate 
opposite leaves 

7. S. carrerei, 

6. S. hoerensis, 

5. S. meriani, 

4. S. paradoxa, 

Schimp. and 

3. S. africana, 

2. S. wardi, 

1. S.gondwanensis, 

9^Bjj ^sd}imv2V009^ 

(o'\ou'\s nsuas) 'joaSnopj puB .ladraiqog 'vxnduozi^og 

410 ilf?' Wills, Notes on the genus Schizoneura, etc. 

of the leaves into sheath-segments. Their distribution in time 
is also of interest, for this type of ScMzoneura appears to have 
almost died out before the advent of Neocalaniites in the Letten- 
kohle and Lower Keuper. It may be that the one type gave 
rise to the other, but this does not seem likely. In this con- 
nection I would like to point out that Halle comments on 
the resemblance and possible relationship of Neocalamites with 
Calamites. In the same way, one may draw a comparison between 
ScMzoneura proper and Grand'-Eury's Calamodendron type of 
Calamite. Thus, the whorls of leaves are separated by long 
internodes and the upper branches probably radiated out in all 
directions, while the leaves themselves had several nerves instead 
of a single median one, all of which facts are points of resemblance 
between the two genera. At the same time we must recognise 
that, until we know more about the internal structure and fructi- 
fication of this important transitional group of the Equisetaceae, 
the relations that they bear, both to the Calamites and to the 
modern Equiseta, must remain a secret. 

Gonclusion. The species so far described as Schizoiieura may 
be divided into two groups. The one has been given the name 
Neocalamites by Halle, and includes S. carrerei, S. hoei'ensis, and 
S. meriani. The other may be termed ScMzoneura, sensu stricto, 
and embraces S, gondwanensis, S. africana and S. pa,radoxa. 
Until we have more satisfactory information about S. ivardi we 
are unable to decide to which group it belongs. 

Mr Lillie, On Petrified Plant Remains, etc. 411 

On Petrified Plant Remains from the JJi^per Coal Measures of 
Bristol. By D. G. Lillie, B.A., Hutchinson Student of St John's 
College. (Communicated by Mr E. A. Newell Arber.) 

[Read 7 February 1910.] 

In working out the flora of the Bristol Coalfield, which con- 
sists entirely of the impressions of fossil plants, I was fortunate 
enough to obtain a small quantity of petrified material. This 
was entirely unexpected, because no other source of structural 
material of Upper Coal Measure Age is known in Britain. Our 
whole knowledge of the anatomy of the plants of this period is 
entirely founded on Lower Coal Measure material from the York- 
shire and Lancashire Coalfields. 

The horizon of the petrified material from the Bristol Coal- 
field is Upper Coal Measures. This is shown by the associated 
impressions, an account of which has recently been published 
elsewhere*. The material was obtained from the base of the 
Pennant Grit at one locality, Staple Hill, three miles to the 
north-east of Bristol. 

A sinking for coal which penetrated for about 300 feet, was 
made a short time ago in this locality and was abandoned in the 
Bristol equivalents of the New Rock Series of Radstock, a short 
distance below the base of the Grit. On this level a massive 
conglomerate was passed through, the exact thickness of which 
does not appear to be known ; but the bed was probably of 
no great thickness. Mr Bolton, F.G.S., Curator of the Bristol 
Museum, who first examined the sinking, pointed out to me 
that plant remains occurred, associated with the pebbles, in this 
conglomerate, and suggested that 1 should collect the material 
for examination. 

At the time when I visited the locality the sinking had been 
abandoned for some time and the supply was found to be very 
limited. It does not appear likely that further material will be 
obtainable. This peculiar conglomerate has not been recognised 
elsewhere in the coalfield. I understand that Mr Bolton will 
publish a full account of this conglomerate, so I need not enter 
into further details upon the subject in this note. 

The plant remains, associated with the pebbles in the sand- 
stone matrix, consist of fragmentary portions of stems and 
petioles, thoroughly isolated from one another and varying greatly 
in size and diameter. They are calcified, and the structure is 
preserved, the preservation being excellent in some cases. 

* Lillie, Geological Magazine, Dec. 5, 1910, Vol. vii. p. 58. 

412 Mr Lillie, On Petrified Plant Remain.s, etc. 

A large number of them have been isolated from the matrix 
and sections cut from them. The greater number of the specimens 
consist of decorticated stems of Cordadtes, showing the pith and 
the secondar}^ wood. This genus appears to be particularly 
abundant in this locality. In addition to Cordaites, at least one 
example of a new member, either of the same or an allied genus, 
has been obtained. The attribution of most of the plants to the 
genus Cordaites is borne out by the fact that examples of the 
characteristic pith casts, Sternbergia (Artesia), of this genus also 
occur in the conglomerate. In addition, a specimen of a well 
preserved Myeloxylon, the petiole of a Medullosa, has also been 
obtained. A contribution on the detailed structure of these 
fossils is in progress. 

Mr Thomas, On the assimilating tissues, etc. 413 

On the assimilating tissues of some Coal Measure Plants. By 
H. Hamshaw Thomas, B.A., Downing College. 

[Read 7 February 1910.] 

The recent work in Fossil Botany has been concerned almost 
entirely with morphological and phylogenetic considerations and 
little attention has been given to the physiological significance 
of the tissues studied. It is, however, very important from all 
points of view to study so far as possible the biology and physi- 
ology of the fossilised plants. This can be attempted by an 
examination of our material from the standpoint of physiological 
anatomy. The process of carbon assimilation is one of the most 
important of the plant's vital activities and is closely connected 
with leaf structure. Very little research has hitherto been done 
on the subject of leaf structure in the Coal Measure period, and 
at the suggestion of Mr Arber, the author is endeavouring to 
obtain more information on this subject. 

The leaves of some members of the Galamocladus section of 
the Calamites have been studied in detail. They are small linear 
structures, almost cylindrical in cross-section. The simpler types 
seldom exceed a length of 3 or 4 millimetres, and were about 
•8 — 1 mm. broad. They were borne in whorls on long slender, 
probably pendulous, stems. In the longer leaves a considerable 
portion of the tissue is composed of thick-walled sclerenchymatous 
elements which replace the mesophyll, forming a strand on the 
adaxial side and increasing in proportions towards the apex of 
the leaf. When this strengthening tissue is absent the leaf tissues 
present a concentric arrangement, the central vascular bundle 
being surrounded first by the bundle sheath and then by the 
pallisade tissue. 

The mesophyll of the leaf is entirely composed of isolated 
cylindrical cells, running perpendicularly out from the bundle 
sheath to the epidermis, and forming a continuous pallisade tissue. 
These cells are often completely separated from each other by 
very large air spaces, and the tissue was consequently of an 
extremely spongy character. Though this system of spaces would 
provide an ample path for the circulation of carbon dioxide, 
it would also probably bring about rapid transpiration. In the 
larger leaves it is noticeable that the air spaces are considerably 
reduced. There are indications that, as in the pallisade tissue of 
modern leaves, the cells were specially modified to absorb a 
maximum of the incident light. 

VOL. XV. PT. v. 27 

414 Mr Thomas, On the assimilating tissues 

The stomata were confined to the adaxial side of the leaf, 
which in the living state was probably also the lower side. Here 
they occur in considerable numbers, one example showing a 
distribution of about 440 per sq. mm. They were about '024 mm. 
long and '018 mm. broad. In shape, the guard cells resembled 
very closely those of modern Equisetums, and in one specimen 
they show also the transverse striations of thickening material, 
which are so characteristic of the recent plants. The guard cells 
are usually level with the surface of the epidermis but may be 
slightly sunk in it. The latter tissue forms a well-marked feature 
in the leaves. 

Towards the centre of the leaf the pallisade cells abut directly 
on the bundle sheath, and are often somewhat enlarged at the 
point of contact. This enlargement is a feature sometimes ob- 
served in modern plants, and Haberlandt has figured a similar 
arrangement in the connection between the "Zuleitungsystem " 
and the " Ableitungsystem " in Gycas circinalis*. There can be 
little doubt that the bundle sheath, termed by Hickf "melasmatic 
tissue," functioned as the patli of conduction for the products of 
assimilation. It is a conspicuous feature in most specimens, 
because its cells are characterised by the large mass of opaque 
carbonaceous matter which they contain. No distinct tissue 
can be recognised which could be called phloem, nor can any 
sieve tubes be made out. Some leaves show thin-walled elongated 
parenchymatous cells associated with the xylem, while in others 
this feature is completely absent. In each leaf, however, the 
amount of assimilation could not have been large, for the leaves 
are very small; the products could easily be conducted the short 
distance to the stem by diffusion through the elongated cells 
of the bundle sheath. 

The cells of the thin-walled inner zone of the cortex of the 
young stems often contain black contents like those of the bundle 
sheath, and it may be suggested that these also were connected 
with the formation of carbohydrates. 

It would appear then that in the Calamites the leaves show 
a structure adapted for carbon assimilation, even though they 
were very small. They were probably produced in large numbers 
and were sufficient to provide for the nutrition of the plant. 

The leaves of other Coal Measure plants are now being ex- 
amined. Some Lepidodendrons possess foliar members in which 
we find a considerable proportion of mesophyll, which may be 
either of a spongy type composed of rather stellate cells, or in 

* Haberlandt, " Verleichende Anatomie des assimilatorischen Gewebesystems 
der Pflanzen," Pringsh. Jahrb. 1882, Taf. vi. fig. 15. 

t Hick, " On the structure of the leaves of Calamites," Mem, and Proc. Man- 
chester Lit. and Phil. Soc. Vol. ix. 1895, p. 179. 

of some Coal Measure Plants. 415 

other cases may bear considerable resemblance to the mesophyll 
of the Calamites. Tissue of the latter type has also been de- 
scribed by Renault* in L. esnostense, where it has the form of 
chains of cells with numerous interspaces and united by short 
transverse branches. 

In material from Shore, Littleborough, Lancashire, leaves 
have been found which are probably identical with a type de- 
scribed by Felix f from Westphalia some time ago. There is no 
record of their previous discovery in this country, and as yet their 
affinities are uncertain. It seems probable that they belong to 
some species of Lepidophloios. They are about 6 mm, across, and 
fragments over 3 cms. long occur. In these the mesophyll appears 
differentiated into spongy tissue and pallisade cells, and thus more 
closely resembles that of the higher plants. 

In so far as the present work has progressed there would 
appear to have been considerable variety in the assimilating 
systems of the different members of the Carboniferous flora, and 
these may be closely compared with those found in living plants. 

* Eenault, Flore fossile d'Autim et d'Epinac, Paris, 1896, p. 179. 

t Felix, J., Westphalischen Carbon Pflanzen, Berlin, 1886, Taf. v. fig. 6. 


416 Mr Beatty, The production of Cathode Particles 

The production of Cathode Particles by Homogeneous Rontgen 
Radiations. By R. T. Beatty, M.A., B.E., Emmanuel College. 
(Communicated b}' Prof. Sir J. J. Thomson.) 

[Bead 21 February 1910.] 

Several physicists have investigated the cathode particles 
produced when Rontgen radiations fall upon various substances. 
The recent work of Cooksey* and Innesf has shown that the 
velocities of these cathode particles are independent of variations 
in the intensity of the Rontgen radiations used, and are also 
independent of the nature of the substance struck, but that the 
velocities increase or decrease with an increase or decrease in the 
penetrating power of the exciting Rontgen radiations. 

The discovery of homogeneous Rontgen radiations, emitted 
by certain metals when exposed to suitable Rontgen radiations, 
enables one to use definite beams which differ widely in penetrat- 
ing power, and it seemed that by using such beams more definite 
information might be gained about the cathode particles emitted 
from metals placed in the path of such beams. 

When a very thin silver leaf was placed in the path of the 
homogeneous radiations described above, cathode particles shot 
out from its surface. It was determined to investigate the 
coefficients of absorption of these cathode particles in air and in 
hydrogen. Hydrogen was chosen on account of its anomalous 
behaviour with regard to ionisation phenomena. 

The radiations from a Rontgen bulb, proceeding in a direction 
normal to the plane of the paper (fig. 1) fell upon the metal 
which acted as radiator. Plates of Fe, Ni, Cu, Zn, As, Sn were 
used as radiators. 

A homogeneous radiation then proceeded from the radiator. 
Part of this entered the cylindrical brass chamber A through the 
thin parchment window. It then passed through the silver leaf, 
and was finally totally absorbed in the thick brass disc DD which 
served as electrode. DD was covered with paper to prevent the 
emission of cathode particles from its surface. 

Another portion of the radiation entered the primary electro- 
scope (fig. 1), which served to standardise the amount of homo- 
geneous radiation emitted by the radiator. 

As the quality of the homogeneous radiation is unaffected by 
variations in the bulb, and as the quantity of radiation entering 
the chamber A is always the same fraction of that entering P 

" Cooksey, Am. Jour. Sci., iv. 24, 1907, p. 285. 

t Innes, Proc. Boy. Soc, Set. A, lxxix., Aug. 2, 1907, 

pp. 442—462. 

hy Homogeneous Rontgen Radiations. 


(for a given radiator), no discordance in the results can arise from 
variations in the bulb. 

The electrode D v^as parallel to L and distant 1 cm. from it. 
D was connected to the gold leaf of the secondary electroscope, 
and could be earthed by a key. The chamber A was kept at a 
potential of 200 volts. 

When the bulb was in action the air between D and L was 
ionised. Thus a charge was given to D, as soon as the connection 
to the earth was broken. The method of experimenting was to 
vary the pressure of the air inside A, and to measure the ionisa- 
tion between D and L corresponding to each pressure. The 
amount of this ionisation was in each case standardised by means 
of the primary electroscope. 

TO "PumP 





Pr irnwryTXect r 04 c o|) e 

Fig. 1. 

This ionisation is due to two causes: (1) Ionisation due to 
X-radiation alone. This has been shown by Crowther* to vary 
directly as the pressure of the air. (2) Ionisation due to cathode 
particles emerging from L. The amount of ionisation due to this 
source will remain constant as long as the pressure is great enough 
to absorb all the particles. When the pressure falls below a certain 
value some of the particles will reach D before being absorbed and 
the ionisation will decrease. 

Fig. 2 shows how the ionisation due to each of these sources 
varies with the pressure, and how the actual curve found is the 
sum of these separate effects. 

Crowther, Proc. Roy. Soc, Ser. A, lxxxii., March 10, 1909, pp. 103—127. 


Mr Beatty, The production of Cathode Particles 

Hence given the actual curve we find the part due to cathode 
ionisation by drawing through the origin a line parallel to the 
straight portion of the curve, and subtracting its ordinates from 
those of the actual curve. This process gives the curve showing 
the increase of cathode ionisation up to a certain pressure. 

The pressure at which the ordinate of the cathode curve is half 
the length of the maximum ordinate gives the pressure at which 
half the cathode particles starting from L reach D. 

Knowing the distance between D and L (1 cm.), the tempera- 
ture of the room, and this critical pressure, we can now calculate 
the thickness of the layer of air at 170 mm. pressure and 15° C. 
tempei'ature, which would absorb one-half of the energy of the 
cathode particles starting from L (Table I, column 1). 

Table I. Air. 

Cathode energy 

Total cathode 


d in cms. 

X in cm.~i 

em erging -f- absorp - 

tion of Z-radiation 

in leaf 

energy produced in 

leaf -^ absorption 

of Z-radiation 


























If we assume that Ge~''^ represents the amount of energy 
which gets through a thickness x (in cms.) of air at normal 
pressure and temperature we can now calculate \, the coefficient 
of absorption of the cathode particles by air. For when 

^ d 

The values of \ are given in column 2. 

Further, since the experimental curves can be split up as 
shown in fig. 2, we can determine the ratio of the ionisation 
caused by the emerging cathode particles to the ionisation due to 
the X- radiation in the layer of air between D and L. For the 
sake of uniformity we shall measure this X-ionisation when the air 
is at a pressure of 760 mm. 

This ratio has really a very simple meaning. Barkla and 
Sadler* have shown that if we take any two substances which 
do not give a homogeneous radiation under the stimulus of a 

* Earkla and Sadler, Phil. Mag., May 1909, p. 751. 

by Homogeneous Rontgen Radiations. 


certain series of Z-radiations, then the ratio of their coefficients 
of absorption for this series of X-radiations remains constant for 
each one of this series. 

Since silver* and airf exhibit no homogeneous radiation when 
stimulated by the range of radiations here employed, we may 
assume that their coefficients of absorption have a constant ratio 
for each X-radiation. 

We shall further assume that the ionisation in air is pro- 
portional to the coefficient of absorption of air. 

Hence ionisation of air oo absorption by air of radiation 
absorption by air oo absorption by silver. 

.•. ionisation of air oo absorption by silver. 

£ii9de ioi{iscitto7i 

Vieny^-^Q of dcr 

Fig. 2. 

Hence the ratio (Table I, column 3) is a measure in arbitrary 
units of the ratio of the energy of cathode particles emerging 
from the silver leaf to the amount of energy absorbed by the leaf 
from the X-radiation. 

From the numbers in Table I, column 3, we can attempt to 
calculate the total energy due to cathode particles produced in 
the whole volume of the leaf when the leaf absorbs a fixed quantity 
of radiation. 

Two assumptions must be made : 

(1) That each cathode particle moves initially in the direction 
of the incident X-radiation. 

(2) That these particles are absorbed according to an ex- 
ponential law in the silver leaf itself. 

These assumptions have not been definitely proved, but there 

* Ihid* loc cit* 

t Beatt'y, Phil. Mag., Nov. 1907, pp. 604—614. 


M?' Beatty, The production of Cathode Particles 

is evidence in favour of both of them, and they are the simplest 
that can be made. 

Now if / be the amount of ionisation in air due to the cathode 
particles which emerge from the leaf, and X the coefficient of 
absorption of these particles in silver, then a simple integration 
shows that \I is the amount of ionisation which would be caused 
if all the cathode particles set free in unit thickness of the silver 
were able to spend their whole energy in ionising air instead of 
being absorbed by the leaf 

Since for any set of cathode particles the absorption in air is 
proportional to the absorption in any other substance*, we may 
use the former value instead of the latter, if we are not compelled 
to use absolute values. 

Hence if we multiply the numbers in Table I, column 3, by 
the corresponding values of A, in column 2, we get numbers giving 
the amounts of cathode energy liberated by different kinds of 
X- radiations when they are equally absorbed in silver. The results 
are given in column 4. 

These numbers are seen to be of the same order of magnitude 
though the numbers in column 3 vary widely. No closer agree- 
ment is to be expected considering the three assumptions which 
have been made in getting this result. 

Hence we are justified in concluding that the amount of energy 
spent by the incident radiation in producing cathode particles is 
proportional to the energy of that radiation which is absorbed by 
the leaf. 

The experiments were now repeated, using pure hydrogen 
instead of air in the chamber A. The results are given in 
Table II. 

Table II. Hydrogen. 


d in 

X in 

Range in H2 
Range in air 

Total cathode ionisation in Hg 
Total cathode ionisation in air 










The first column gives the thickness in cms. of the layer of 
hydrogen at 760 mm. pressure and 15° C. required to cut down 
the energy of the cathode particles to half its value. 

* Lenard, Wied. Ann., lvi., 1895, p. 255. 

hy Homogeneous Rontgen Radiations. 


Column 2 gives the coefficients of absorption by hydrogen. 

Column 3 is obtained by dividing the values of A, given in 
Table I by the corresponding values in Table II. It will be 
seen that the ratio increases as the cathode particles become more 

Column 4 gives the ratio of the total ionisation produced by 
a given bundle of cathode particles in hydrogen to that produced 
by the same bundle in air. The I'atio is unity luithin the limits of 
experimental error. 

In Table III are added some data previously found for cathode 
rays. It will be seen that the constants relating to the cathode 

Table III. 

Velocity of corpuscles 
expressed as due to a 
potential fall in volts 

X for air 


Range in Hg 
Eange in air 










particles due to the Sn radiation are very close to those found by 
Lenard for corpuscles possessing a velocity due to a drop of potential 
of 30,000 volts. 

Relation between the absorption of the cathode particles by air 
and the absorption of the existing X -radiations by aluminium. 

This relation was found to be linear, and is shown in fig. 3. 
The abscissae are taken from figures due to Barkla and Sadler*, 
with the exception of that relating to Sn, for which radiation 

it was found by the author that - = 1*65, the absorber being 


Relative ionisation in air and hydrogen due to homogeneous 
X -radiations. 

The ionisation in hydrogen due to soft JT-radiations is so small 
that the straight portion of the typical curve shown in fig. 2 was 
almost horizontal. A separate set of experiments was made to 
determine this ionisation accurately. The silver leaf was removed 
from the chamber A and the plate electrode replaced by an 
aluminium wire bent into a ring. The ionisation observed in the 
chamber when filled with hydrogen and air respectively was then 
determined. The results are given in Table IV. 

* loc. cit. 

422 Mr Beatty, The production of Cathode Particles, etc. 

Table IV. 


lonisation in hydrogen 

lonisation in air 







2 5 

7p of X«ro(dmttOTi iu/l^ 



Fig. 3. 

Note. In a recent communication to Nature (October 28, 
1909) Sadler has determined various relations among the cathode 
particles excited by homogeneous Rontgen radiations. His results 
do not in all cases agree with the relations here described. 

I have much pleasure in thanking Sir J. J. Thomson for his 
interest in this investigation. 

Mr Bateman, Solution of a system of differential equations, etc. 423 

The solution of a system of diffh-ential equations occurring 
in tJie theory of radio-active transformations. By H. Bateman, 
M.A., Trinity College. 

[Read 21 February 1910.] 

1. It has been shown by Prof. Rutherford. * that the amounts 
of the primary substance and the different products in a given 
quantity of radio-active matter vary according to the system of 
differential equations, 


~Tr — ~X^Q ~ XsSi 


= X-xR — \aT 


where P, Q, R,S,T,... denote the number of atoms of the primary 
substance and successive products which are present at time t. 

Prof Rutherford has worked out the various cases in which 
there are only two products in addition to the primary substance, 
and it looks at first sight as if the results may be extended to any 
number of products without much labour. 

Unfortunately the straightforward method is unsymmetrical 
and laborious, and as the results of the calculations are needed in 
some of the researches which are being carried on in radio-activity 
the author has thought it worth while to publish a simple and 
symmetrical method of obtaining the required formulae. 

2. Let us introduce a set of auxiliary quantities p (x), q (x), 
r{x), ... depending on a variable x and connected with the 
quantities P {t), Q (t), R (t), ... by the equations, 

y. 00 -.00 

p{x)= e-'''P(t)dt, q(x)=\ e-''^Q{t)dt (2). 

It is easily seen that 




-P{0) + x I e-^* P (t) dt 

— Po + Xp, 


Radio-activity, 2nd edition, p. 331. 


4-24 Mr Bateuian, Sohdion of a system of differential equations 

where p is written for pix), and P^ for P (0), the initial value 

Multiplying equations (1) by e~^\ and integrating from to 
X with regard to t we obtain the system of equations 

xp-P^^- \,p \ 

^q -Qo = \p - Xo^- 

xr — Pfl = ^29' — '^■i'}' 
xs — So = ^sr — X^s ^ 
from which the values of ^, q, r may be obtained at once. 

If Qu = jRo = 'So = • • • = 0, i.e. if there is only one substance 
present initially, we have 

^^'x'+Xi' ^~ {x + \)(x + \o)' ^~{x + Xi) (x + Xa) {x + Xs) ' 

and for the /itli product 

/ \_ XiXq ... A,t_i-ro 

''^^~ix~+x,){x + x.;)... (x + Xn) ^ ^• 

Putting this into partial fractions, we have 
V {x) = — — — H -— - + 

where Ci = 

X + Xi X + X2 '" X + Xn' 

Xi X2 • • • ^»-i Pq 

(X2 ~ ^1) (X3 ~ \) • • • (^M — ^1) 

X1X2 ... X,j,_iPo |- (6). 

' ~ (Xi - X3) (X3 - X„) . . . {Xn - X,) 

- etc. 

To obtain the corresponding function N (t) we must solve the 
integral equation 

v(x)=l e-*< N {t) dt. 

Now it has been shown by Lerch* that there is only one 
continuous function N (t) which will yield a given function v (x) ; 
hence if we can find a function which satisfies this condition it 
will be the solution of our problem. It is clear, however, that 

1 r" 

+ X Jo 

x + 
hence the above value of v (x) is obtained by taking 

N (t) = CiB-^^* + 026-"'*+ ... CnC-^-^ (7), 

where the constants have the values given by (6). 

* Acta Mathematica, 1903, p. 339. 

occurring in the theory of radio-active transformations. 425 

In the case when Q (0), R (0), . . . are not zero, we have 

^ « + Xi' ^ {so + Xi) (x + Xi) oc + Xo 

X.1X2-P0 , X^^^Q 

r = 





{oc-{-Xi){oG + X2)(sc + Xa) {x + Xz){x + \s) (os + Xs) 
etc. / 

and we may obtain the values of P, Q, R by expressing these 
quantities in partial fractions as before. 

The complete solution for the case of a primary substance P 
and three products Q, R, S is 

R = 

S = 

A-j A,2 -to 

(Xg — Xi) (X-s — Xi) 

e-^if + 




X1X2X0 Xg^/p 

_(Xi — X2) (Xg — X2) Xj — X. 
X1X2P0 X2Q0 

L (^1 ~ ^3) (X2 — X3) X2 — X3 

+ Ro 







{X, - X2) (X3 - X2) (X4 - X2) (X3 - X2) (X, - X2) J 

Xi X2 X3 -T X2 X3 (j^o 

_(Xi — X3) (Xg — X3) (X4 — X3) (X2 — X3) (X4 — X3) 


Xa Xq 

Q-ht + 

Xi X2 X3 Pq 


(Xi - X4) (X2 - X4) (X3 - X4) 


+ So 


(X2 — X4) (X3 — X4) X3 — X4 

The solution may evidently be obtained by superposing the 
solutions of the cases in which the initial values of P, Q, R, S are 
given by 

(1) P(0) = Po, Q{0) = 0, R{0) = 0, S{0) = 0. 

(2) P(0) = 0, Q(0)=Qo, R{0) = 0, S{0) = 0. 

(3) P(0) = 0, Q(0) = 0, R(0) = Ro, S{0) = 0. 

(4) P(0) = 0, Q(0) = 0, P(0) = 0, ;Sf(0) = ^o. 

The method is perfectly general, and the corresponding 
formulae for the case o( n—1 products may be written down at 
once by using (6). 

The general formula covers all the four cases {Radio-activity, 
pp. 331 — 337). For instance in Case 2 when initially there is 
radio-active equilibrium, Ave have 

Uf) = XjPo = XnQ^^ = XgPo = X^Oq, 

426 Mr Bateman, Solution of a system of differential equations 
The solutions are then 

(Xo - Xi) (X, - Xi) (Xi - Xo) (X3 - X,) 


Xo (Xi - Xo) (X, - X3) 

o X2 XgWp _^ ^ 


(Xj — Xg) (X3 — X2) (X4 — Xg) 

Xi Xo yin , . 

-I 1__2_0 ^_},^f 

(Xj — X3) (X2 — X3) (X4 — X3) 

_! XiXgXaTlQ ^_^^^^ 

(Xi — X4) (Xa — X4) (Xg — X4) 

The solution for the case of w— 1 products is given by 
N = 'Ecre-^'-*, 
where the constants c,. are obtained by expressing 

X1X2X3 ... \ n—i 

CC (x A- Xi) (x + X2) ... (X + \n) 

in partial fractions. 

The method by which the solution of the system of differen- 
tial equations has been obtained is really of very wide application 
and may be employed to solve problems depending on a partial 
differential equation of the form 

dt \dx' dy' dz' '") ' 
provided the initial value of V is known. 
For if we put 

u{s)=\ e-'*V{t)dt, 

f^ dV 
su{s)-Vo= e-''irdt, 
Jo ot 

it appears that u{s) satisfies the partial differential equation 

^(8l'3i8i-)^+»+''« = « W- 

Further, if V satisfies some linear boundary condition which 
is independent of t the function ti will generally satisfy the same 
boundary condition. This function (u) must be obtained from the 

occurring in the theory of radio-active transformations. 427 

differential equation (10) which is simpler than (9), inasmuch as 
it depends upon fewer independent variables, 

Tn many cases the solution of the integral equation 

n (s) = I e-«' V(t) dt 

may be calculated by means of the inversion formula * 

where c is a contour which starts at — oo at a point below the 
real axis, surrounds all the singularities of the function u (^) and 
returns to - oo at a point above the real axis, as in the figure. 

The conditions to be satisfied by u (^) in order that this 
inversion formula may be applicable have not yet been expressed 
in a concise form. 

The formula may be used to obtain the solution of a problem 
in the conduction of heat when we require a solution of 

dx^ ~ dt' 

which satisfies the boundary conditions 

F= when x=0 and x = a, 

V =f(x) when ^ = 0. 

The solution found in this way is identical with the one given 
in Carslaw's Fourier-' s Series and Integrals, p. 383. 

* A particular case of this formula has been given by Pincherle, Bologna 
Memoirs, 10 (8), 1887. 

428 Mi^ Buiifiside, On double-sixes. 

On double-sixes. By W. Burnside, M.A., F.R.S. 
[Received 7 February 1910.] 

The configuration of twelve lines, known as a double-six, arises 
naturally in connection with the theory of cubic surfaces. Its 
connection with the theory of quadric surfaces has not, so far as 
I know, been investigated. It is the object of the present note 
to establish the existence of a double-six from what I believe to 
be a fresh point of view, connecting it with a pair of quadric 
surfaces that stand in a special projective relationship to each 
other. A word of explanation must be given of the digression in 
I 3. The theory of quadrato-quadratic equations has been very 
completely worked out; but the particular relation here required 
could not be quoted in a convenient form. It has therefore been 
established directly. 

1. Let 8, 8' be two quadrics. On each choose one of the two 
sets of generators : and let \ be the parameter that distinguishes 
one of the chosen set on 8, and //, the corresponding quantity for 
8'. A generator of 8 meets 8' in two points, through each of 
which will pass one generator of the chosen set on 8'. In other 
words, if \, fi are parameters of two intersectiug generators on 
8 and 8', they are connected by an equation which- is quadratic 
in both \ and yu,. Denote this equation by 

f{\H') = (i). 

Let yu,_i, fio be the roots of this equation when X is Xq; ^o. \ the 
roots when /j, is yu-o, X_i, \ the roots when /j, is /jb_-^; and so on. 
Then there arises an, in general, unending series of quantities 

. . . X_oyu._3X_i/i_i Ao/U'o^i)"'i^2 (ii)» 

all of which are rationally determinable in terms of any two 
consecutive ones. Corresponding to this series there is an, in 
general, open polygon whose sides belong alternately to the 
chosen generators on 8 and the chosen generators on 8'; and 
no side of the polygon meets any other except the two which 
immediately precede and follow it. The theory of an equation, 
quadratic in both variables, such as (i) is well known. Starting 
from an arbitrary pair of values that satisfy it, the series of 
values (ii) is in general unending, but if it is periodic for some 
chosen initial value of X (or /x), i.e. if it is of the form 

. . . X,i/l.,i,Xo/ioXi/ii . . . i^tif^n • ■ •} 

then it is periodic for every initial value. Suppose now that 
the quadrics 8, 8' are such that the polygon is a (gauche) 

Mr Burnside, On double-sixes. 429 

hexagon. Then the existence of a double-six implies that when, 
with the remaining set of generators on S and the remaining set 
on S' the same construction is carried out, the polygon is again 
in this case a hexagon. Conversely, a proof that this latter 
polygon is a hexagon establishes the existence of a double-six, 

2. Any two arbitrary quadrics can, by a suitable projection 
(which may be imaginary), be brought to the forms 

x'-y'- a?z' -I- hH'' = 0, 

cV - d^ -z^+t'' = 0. 
A generator of a chosen system from each is given by 

X + y + \ {az -\-ht) = Q\ 

X{x — y) -\- az — ht = \ 
and ex -\- dy + fi{z + t) = \ 

fi (ex — dy) + z — t = 0. 

The condition that these should meet is easily found to be 

XV + ^ (X' + At') + BXfi -1-1 = 0, 

(a + b)(c + d) r. . cibcd + 1 
when . A = ) rr^ k , B = -4t 

{a-b){G-d)' {a-b){c-dy 

The equations to the two other sets of generators, and the 
corresponding conditions for them are obtained by writing — 6 
and —diovb and d. It is to be noticed that writing — X for X 
merely changes the sign of B. 

/ 1 — i^ 2^ \ 

3. The tangent at y^Y^r^, r j to x'^ + y'^ = r^ is 

x{\-t^)-\-yn = r{l + 1?). 
If this meets {x + af + y^ = R^ in the point 

then \(R-a)-(R + a) t'^] (1 - t^) + ^Rtt' = r (1 4- ^') (1 4- P). 

Put t = ms, t' = ns'; 

then rnhv" (R-r + a) s'^s'^ -m?(R + r- a) s"" -n''(R + r + a) s'^ 

+ 4iRmnss' + R — r — a = 0. 
If mV {R-r + a) = R-r — a, 

and ni'(R + r- a) = n'^(R + r + a), 

the equation is 

s^s'^ + A(s^ + s'2) + Bss +1 = 0, 

where A^=h- f- -, B^ = — 

{R-ry-a"' {R-ry-a" 

VOL. XV. PT. V. 28 

430 Mr Burnside, On double-sixes. 

The equation connecting \ ^ is the same as that connecting 
s, s'. Hence if the polygon whose sides lie on the two quadrics 
is a hexagon, the circles must be such that the sides of a triangle 
inscribed in the second circle touch the first. The conditions for 
this are either 

(i) a' = R^- 2Rr, or (ii) a^ = R' + 2Rr. 

In the first case, 

^" :^2 ' ^^ — y:r~' 

giving A^ — 1 — ± B. 

In the second case, 

r^ 16R'^ 

^■' - r^ _ 4,Rr ' ^"~ r-"- ^Rr ' 


A^-1 = + AB. 

(a + b)(c + d) . ahcd + 1 

{a-b){c-d)' {a-b){c-d) 
satisfy one of these relations, then obviously 
(a — b)(c — d) abed + 1 

{a + b)(c + d)' (a + b){c + d) 

satisfy the other. In other words, if for a chosen pair of sets of 
generators of the quadrics the polygon is a hexagon, then it is 
also a hexagon for the other two sets. As pointed out above, 
this is equivalent to establishing the existence of a double-six. 
5. If the two quadrics are taken in the usual canonical form 
ax^ + by^ + cz^ + df = 0, 
a'x^ + b'y"" + ez" + d'f = 0, 
it will be found that the above condition 

A'-1 = ±B, 

which ensures that a double-six lies on them, may be expressed 
irrationally in the form 

1 1 1 ^ 

'^abo'd' + '^a'b'cd '^acb'd' + "Ja'c'bd ^/adb'c' + Va'd'ftc 

Mr Edwards, On the Procession and Pupation, etc. 431 

On the Procession and Pupation of the Larva of Cnethocampa 
pinivora. By T. G. Edwards, B.A., Emmanuel College. (Com- 
municated by Mr H. H. Brindley.) 

[Bead 21 February 1910.] 

The following note is a summary of certain observations made 
during a fortnight spent at Arcachon, between the 18th and 31st 
of March, 1909, a visit which I undertook at the suggestion of 
Mr Brindley with a view to clearing up certain points with regard 
to the processional larva of Cnethocampa pinivora. 

The habits of this peculiar larva were first studied by Reaumur 
in 1736, who treated the subject in considerable detail; but as his 
material was all conveyed by coach from Bordeaux to his house at 
Paris, the conditions under which his experiments were performed 
were necessarily somewhat artificial. Ratzeburg also described 
the life history, while in the last fifteen years Fabre has recorded 
his observations on all stages of this moth, confirming many of 
Reaumur's results and adding much to his account of this insect. 
Lastly, a paper by Mr Brindley appeared in the Proceedings of 
this Society for 1906. In this was given a detailed account of the 
behaviour of a certain procession which came under the writer's 
observation, together with certain other points which supple- 
mented Fabre's description. 

On warm days in March and April the processions of Cnetho- 
campa pinivora are frequently to be observed in the neighbourhood 
of the Pine Woods of the Landes, where their nests form prominent 
objects among the branches. 

The procession is one of single file, the larvae being arranged 
in head to tail contact. The whole moves along a silken thread 
which is commenced by the leader and added to by all the larvae 
in succession. 

The number comprising a procession varies greatly, and though 
I saw many processions, I only encountered three which exceeded 
one hundred in number. The largest of these was crushed upon 
the pavement of a road near the woods, but it measured 26 ft. and 
must have contained at least 260 larvae. 

Nature of the Procession. 

(a) Priinite. Several experiments were made with a view to 
determining how far the primite may be regarded as the true 
leader. It was found — as Fabre states — that any larva could 
function as primite, and that all individuals in the procession 


432 Mr Edwa7'ds, On the Procession and Pupation 

were alike in this respect. Yet — as Avill be seen later — it was 
found that a particular larva, when once entrusted with this 
position, usually retained it. On one occasion, however, I saw 
a voluntar}' change of leader, the primite detaching himself and 
becoming inserted at the fifth place. It seemed probable, too, 
that the primite was capable of taking a real initiative in certain 
cases, the remainder following him whether influenced by the same 
stimuli or not. This was shown to be the case in 

(1) The selection of a path. 

(2) Burrowing for pupation. 

(3) Forming of a "circulating mass." (This term is explained 


In the first case at least two external conditions seem to 
influence his choice, viz. light and surface. This was suggested 
in the case of a small procession of seven which came under my 
observation, I threw the whole procession into the shade and 
determined the path taken by the primite by causing a reflected 
ray of light to be cast beneath his head. The procession followed 
the reflected ray, although only the primite could have been 
influenced by this stimulus. In the case of processions which 
burrowed for pupation the primite was frequently observed to 
test the ground Avith his mandibles before a circulating mass — 
the formation always adopted before burying — was formed. 

The term " circulating mass " is used in Mr Brind ley's paper 
to denote the assemblage of larvae moving among each other ; 
but the assemblage, as a whole, remaining on the same spot. 

In the formation of the circulating mass, the primite seemed 
to be taking the initiative by turning his body sharply round 
into a position parallel to that of the second : and if a procession 
was reformed without pupation the same larva usually took the 
lead. Thus it appears that though any larva can take up the 
duties of the primite, yet the primite does in a real sense lead the 
procession, the satellites following whether influenced by identical 
stimuli or not. At nightfall — according to Fabre — the procession 
usually returns to the nest, the primite wandering round until 
he strikes the outward-bound thread. I never observed this 
proceeding, but if Fabre be correct it would seem that the primite 
is capable of exercising choice in this respect. In all the cases 
I examined the leader refused to walk along any foreign thread— - 
whether artificial (e.g. silk thread frayed out) or that of another 
procession — which I placed in his path. 

In addition to light and surface, the desire to pupate and 
temperature might be suggested as factors influencing the primite 
in his movements : and — as Fabre suggests — the occurrence of 
processions at all is dependent upon atmospheric conditions ; for 
in bad weather the larvae remain in their nests. 

of the Larva of Cnethocampa pinivora. 433 

(b) The function of the Thread in the Procession. In the 
case of a small procession, with the aid of a lens it was easy to 
see that each larva secreted its own thread, which was passed 
between the pro-legs of the terminal segment. When the path 
of the procession became irregular the multiple nature of the 
thread was occasionally observed. 

In the case of a large procession of 158 the thread became 
very thick, in some places a band of silk some 2 or 3 mm. in 
thickness being formed. In this case again the multiple nature 
of the thread was clearly discernible. In spite of this it does not 
seem that it is the thread which guides a satellite in procession 
so much as the tail of the larva in front. The following observa- 
tion supports this view. 

Two sections of a procession — each consisting of seven larvae — 
were progressing in the same direction, separated by about 
18 inches : the second eventually caught up the first and joined 
it, though it did not at any time follow the silk thread laid down 
by the latter. On the contrary that thread was crossed several 
times, and joining up only occurred when the primite of the 
second in his wanderings accidentally struck the sixth larva of the 
first procession ; when he stopped immediately until the last larva 
had passed and joined on in the right place. 

The evidence of artificial breaks is of interest in this connec- 
tion. It appeared in all cases examined that touch rather than 
sight was the chief guide to the satellites. When larvae were 
removed from the middle of a procession, together with the 
thread beneath them, joining-up always occurred if the leader 
of the hinder portion actually came into contact with any part 
of a larva in front. If the thread were left, joining-up was more 
frequent, but if the break were small it occurred whether the 
thread were removed or not. 

These observations tend to show that normally the chief factor 
in keeping a procession together is the head-to-tail contact of the 
larvae. The thread is of relatively small importance in this 
connection, and serves rather as a guide to the primite on his 
return journey to the nest. But the fact that joining-up occurs 
more readily in the case of small breaks, when the thread is not 
removed, would seem to indicate that the touch of the thread 
may under certain conditions act as a guiding influence to the 

Method of Formation of the " Circulating Mass." 

When on the march, processions were frequently observed to 
form " circulating masses." This formation is usually adopted 

434 Mr Edwards, On the Procession and Pupation 

immediately before burrowing for pupation : but at other times 
it may result from a variety of causes, amongst which may be 
mentioned fatigue and external interference, and sometimes for 
no apparent reason at all. Fabre suggests cold and darkness as 

When I caused a small procession to circulate in a closed 
orbit, a circulating mass was formed after 2^ revolutions by the 
gradual diminishing of the diameter of the circle, a process which 
tended to crowd out some of the larvae. From this mass a pro- 
cession was subsequently reformed. When formed from a straight 
procession the method of procedure is somewhat complicated. 
The primite appears to start the formation by assuming a zig-zag 
mode of progression, which is followed for a time by the satellites. 
The arrangement soon becomes obscure and difficult to follow, 
but there are certain noteworthy features in the behaviour of the 

On entering the mass the larvae do not come to rest, but 
continue to move slowly and in a very characteristic way, all the 
time moving their heads rapidly from side to side and depositing 
their threads. If the procession be a large one, the satellites 
entering into the newly-forming mass soon begin to crowd one 
another out in their efforts to reach it, until ranks of four or five 
deep are formed. The thread in these places takes a similar 
course. During the day the circulating mass formation may be 
maintained for an hour or two ; but if at the end of that period 
the larvae have not begun to burrow, it is usually abandoned in 
favour of the procession. 

The manner in which the procession is reformed is of consider- 
able interest. By marking alternate larvae (by means of fine sand 
or flour scattered over the dorsal papillae) I found that the 
original order of the procession was not retained ; but in every 
case I observed (five different processions *) the primite of the 
resulting procession tuas the same as that which went into the 
circulating mass. 

Shortly before the primite sets out a rough kind of arrange- 
ment is sometimes to be observed in the mass, many of the larvae 
being arranged with their heads directed towards the point at 
which the procession is to start. The whole process of reformation 
is a very orderly one, though the order in which the larvae "fall in'*' 
is not in every case obvious. 

In the case of a large procession which I photographed in the 
act of reforming the single-file formation, there was an arrange- 
ment of larvae four or five abreast in the neighbourhood of the 
mass, similar to that observed during its formation. 

* The largest a procession numbering 57 larvae. 

of the Larva of Cnethocampa pinivora. 435 

Purpose of the Circulating Mass. 

It is possible that the circulating mass is sometimes formed 
for the purpose of pupation, but again abandoned for the normal 
procession on account of the unfavourable nature of the ground 
in the spot selected. But this explanation cannot apply to the 
majority of cases, for processions are of normal occurrence through- 
out the insect's larval existence. 

Whether or not the circulating mass be a "rest formation" 
(as has been suggested) it is not impossible that it may possess 
other advantages as well. The facts already mentioned suggest 
the possibility of there being a regular arrangement within the 
circulating mass itself In this case the formation might be a 
means of altering the order of the larvae whilst retaining the 
same leader. Other facts may be mentioned pointing to the 
same conclusion. Processions arranged artificially, by removing 
larvae at random from a mass and placing them in a position 
of head-to-tail contact, were not found to retain their original 
order for very long. A circulating mass was always formed and 
a different order arranged for the subsequent procession. The 
formation of a mass, in this case, however, was due probably to 
external interference rather than to any fixed habit of altering the 
order of the procession. 

Method of Pupation. 

Larvae which had become isolated, from any cause, were 
observed to bury themselves in the soft sand by means of their 
mandibles; but as a general rule processions seemed to burrow 
collectively in the following way. A circulating mass was first 
formed in a position which the primite apparently selected, after 
testing the consistency of the sand with his mandibles. On two 
occasions, which came under my observation, the process differed 
slightly, in that the original procession voluntarily broke up into 
several smaller processions of twenty or so each — in a manner 
similar to that described by Fabre — each of which formed a 
circulating mass and buried itself independently. As soon as the 
circulating mass was formed the whole commenced to rotate, thus 
producing a depression in the sand which gradually deepened. 
The sand was at the same time loosened, and some was thrown up 
on to the top of the mass. All the while the larvae were deposit- 
ing their silk threads until a regular network was formed round 
the mass, in which sand became entangled. In some cases the 
lower larvae appeared to assist in the process by attacking the 
sand beneath with their mandibles. As the process continued 

436 3[r Edwards, On the Procession and Pupation, etc. 

the whole mass gradually became engulfed, and finally, in the 
course of a few da3's, reached a depth of several inches. 

When large processions became buried in this way, without 
first fragmenting, bundles of considerable size were formed. 
I discovered one numbering more than 100, buried at a depth 
of 3 inches. Some of these I removed with the sand containing 
them. These completed pupation 19 days after burrowing. 


The facts recorded in the previous observations all seem to 
support the conclusion that, though the individuals of a procession 
may act alike when influenced by the same stimuli, yet each larva 
is capable of independent action, (Cf. voluntary chauge of leader, 
action of primite under special conditions, fragmentation of pro- 
cessions occasionally preceding pupation, etc.) 

If this be so the procession cannot be said to act in any real 
sense as a single individual. 

Fabre states that the poisonous properties of the larval epi- 
dermis are exceedingly severe in some cases ; yet, if this be true, 
the effect must depend largely upon the individual. I was not 
affected at all, though I was handling the larvae for several hours 
at a time. Mr Brindley also found no irritation from the larvae, 
though the Tachinid flies which he observed laying their eggs in 
a procession were noticed by him evidently to fear and avoid the 
hairs. I was told, ho\vever, by an inhabitant of the district, that 
some persons were subject to a msh at the time when the pro- 
cessions were abroad. This is said to be produced by the fine red 
hairs of the dorsal papillae which float in the air. 


Reaumur, 1736, Memoires pour VMstoire des Tnsectes, li. pp. 149 — 161. 
Fabre, circa 1898, Souvenirs Entomologiques, ser. vi. pp. 298 — 392. 
Ratzeburg, 1840, Forst-Insecten, ii. p. 128, and Stettiner Entomologische 

Zeihing, p. 40, 
Brindley, 1906, Proceedings of Camb. Phil. Soc. Yol, xiv. Part I. 

Mr Glasson, Secondary Rontgen Rays from Metallic Salts. 437 

Secondary Rontgen Rays from Metallic Salts. By J. L. 
Glasson, 1851 Exhibition Scholar of Adelaide University, Gon- 
ville and Caius College. (Communicated by Prof. Sir J. J. 

[Read 14 March 1910.] 

It has been shown by Barkla that when an element of atomic 
weight greater than that of Calcium is struck by a primary 
X-ray beam of suitable hardness, then the secondary X-rays 
emitted by it form a homogeneous beam characteristic of the 
radiating element. 

The object of the present experiments was to determine 
whether the nature of this characteristic secondary X-radiation 
is affected by the state of chemical combination of the element. 

Barkla made some experiments to test this point (Phil. Mag. 
June 1906), but that was before the conception of "character- 
istic homogeneous radiation" was introduced. The enormous 
simplification brought about by its introduction, makes further 
experiments interesting and their interpretation simple. 

In particular it was desired to investigate the effect of a 
change in the valency of the metal upon the characteristic 
radiation from it. 


The arrangement of the apparatus is shown in figure 1. The 
metal or salt to be examined was placed at A, the salt being 
contained in a thin paper tray about 1 cm. deep. B and G are 
two thick lead screens, 20 cm. apart with apertures 2 cm. square 
cut in them. The rays enter the ionisation chamber D by a 
window of aluminium leaf W, and the ionisation produced is 
measured by a Wilson electroscope and a stop watch. No balance 
chamber was used as it was found that the coil, fitted with a 
hammer break, gave a very constant discharge; the variations 
in a series of consecutive readings amounted to about two or 
three per cent. 

The screens for absorbing the rays were placed at B. They 
were of aluminium when an absolute determination of the ab- 
sorption coefficient was required; but in some cases filter papers 
were used when only comparative measurements were required. 

The absorption curve was determined in the same way as that 
used by Barkla in his work on homogeneous X-rays. The per- 
centage absorption caused by a given screen (II) was measured, 
after different proportions of the beam had laeen previously 

438 Mr Olasson, Secondary Rontgen Mays from Metallic Salts. 

absorbed by the screen (I). If a curve is plotted, having as 
ordinates the percentage drop caused by the fixed screen (II), and 
as abscissae the amount previously absorbed by screen (I), then 
if the beam is absorbed exponentially, the curve obtained will be 
a straight line parallel to the cc axis. 


,to tells. 

200 volls. 

Fig. 1. 


Some of the curves obtained in this manner are shown in figs. 
2, 3, 4, and 5. 

The curves obtained when the radiator ^ is a pure metal 
are straight lines. These are inserted for comparison. The 
curves obtained with metallic salts are all of the same Sfeneral 
nature. They are initially horizontal and then tend downwards. 
The point at which the curves begin to show this downward 
tendency depends on the salt used and on the hardness of the 

Mr Glasson, Secondary Rontgen Rays from Metallic Salts. 439 


440 Mr Glasson, Secondary Rontgen Rays from Metallic Salts. 

The value of the absorption coefficient calculated from the 
initial straight portion is always the same as that obtained for 
the characteristic radiation from the pure metal. The radiation 
from the salt thus consists of two parts : 

(i) the homogeneous radiation from the metal, 
and (ii) mixed with this is a " scattered " radiation due to the 

acid radicle considerably harder than (i). 
The proportion of this scattered radiation varies with the hard- 
ness of the bulb. It is generally very small and hence does not 
evidence itself until the radiation has been very much reduced 
by screening. This has the effect of cutting off the soft " homo- 
geneous " radiation much more than the hard " scattered," and 
hence the latter is shown to better advantage. The smallness of 
the amount of scattered radiation due to the light atoms is well 
shown in the case of Ammonium ferrocyanide. In this salt the 
weight of iron in the molecule is only about one-sixth of the 
whole. Yet the radiation due to the light atoms does not evi- 
dence itself until a considerable portion of the beam has been 

The information supplied by these curves may be summarized 
thus : 

(1) The value of the absorption coefficient for the metallic 

radiation is unaffected by its combination with an acid 

(2) It is independent of the valency of the element in the 

compound. This is well shown by the series of iron 
compounds FeSOi, Fe304, and FeaOg. 

(3) The element may even occur in the acid radicle itself 

without affecting the value of A,. 


In this way it is possible to determine \ for some metals which 
it is impossible or inconvenient to use in the uncombined state. 
This has been done in the case of Manganese. The salt used 
was the sulphate ; the curve is shown in fig. 5. The value of X 
obtained from the initial part of the curve is 100. This value 
agrees with that predicted from its atomic weight, using Barkla's 
curve {Proc. Camb. Phil. Sac. xv. 257). 

I desire to thank Sir J. J. Thomson for his interest in these 

Mr Glasson, Secondary Rontgen Rays from Metallic Salts. 441 





10 20 iO 40 SO 60 70 80 90 

Fig. 3. Screen (II) = Aluminium (pd = -017). 




10 20 30 40 SO 60 70' gO 90 

Fig. 4. Screen (II) = 5 Filter papers. 







20 30 10 50 60 70 SO 90 

Fig. 5. Screen (II) = Aluminium (pd- -008). 

442 Mr Growther, On the Transmission of ^-rays. 

On the Transmission of ^-rays. By J. A. Crowther, M.A., 
St John's College. 

[Read 14 March 1910.] 

I 1. The problems connected with the transmission of /8-rays 
through matter are of considerable theoretical importance. Un- 
fortunately they are involved at present in considerable obscurity, 
and a fairly extensive study by various experimenters has so far 
only served to demonstrate the complexity of the phenomena. 
The present paper deals only with a few of the many questions 

§ 2. The first question to be considered is the nature of the 
absorption itself. The absorption of the /3-rays is almost invariably 
measured by finding the diminution in the ionization produced 
by them in some suitable ionization chamber, when various 
absorbing media are interposed in their path. This absorption 
may be due to two causes : — 

(1) to a loss of velocity by the ;8-particles, such as is found 
to take place during the absorption of the a-rays ; 

(2) to an actual decrease in the number of the /8 -particles 
themselves, due either to stoppage or deflection. 

To decide this question it is necessary in the first place to 
determine the velocity of a homogeneous beam of ^S-particles 
before and after transmission through a suitable thickness of 
absorbing material. 

A certain amount of indirect evidence already exists on the 
subject. In 1907 H. W. Schmidt* performed an experiment 
which at the time seemed to prove conclusively that the yS-rays 
suffered no change of velocity even when transmitted through 
very considerable thicknesses of absorbing material. The essential 
features of his method are simple, and may be described here as 
they form the basis of the methods employed in the present 

Three circular holes (fig. 1) are made in three lead screens, so 
as to define an arc of a circle of suitable radius. The system is 
placed between the poles of an electromagnet so that the magnetic 
field is perpendicular to the plane of the circle. By a suitable 
adjustment of the strength of the field a beam of /3-rays entering 
the magnetic field at A can be made to describe the circular path 
AGB, and will produce ionization in a chamber placed at B. 
The velocity of the rays transmitted through this system is known 
from the value of the magnetic field, and the radius of curvature 
of the path, 

* Phys. Zeit. Vol. viii. p. 371. 

Mr Crowther, On the Transmission of ^-rays. 


Schmidt placed at J. a screen covered with radium E ; 
measured the ionization produced above B, for different values 
of the magnetic field, and so obtained a curve connecting the 
intensity of the radiation passing through B with the magnetic 
field. The curve he obtained shows a fairly sharp maximum 
ionization for a certain definite field from which it falls away 
gradually to zero, as the field is increased or diminished. 

Various thicknesses of aluminium were then interposed between 
the radium E and the aperture A and the experiment repeated. 
In every case the curves, though decreasing in height as the 
absorption increased, were exactly similar in shape and there was 
no perceptible shift of the maximum in either direction. From 
this result it was argued that no change in the velocity of the 
rays occurred during their passage through the aluminium. 

There is, however, a certain ambiguity connected with the 
use of the magnetic deflection method, which under the best 
of circumstances can only be minimised, and never completely 

If the apertures have a finite size, as must always be the case 
in practice, the path J. (75 is not the only possible path for rays to 
follow in order to emerge through B. A little consideration will 
show that rays of uniform velocity, but entering the field obliquely, 

444 Mr Crowther, On the Transmission of fi-rays. 

may be transmitted through the system along paths such as acb 
or a'c'h' , even when the field is too strong or too weak to deflect 
the rays, incident normally, along the path AGB. In this way 
even if the rays are of uniform velocity to begin with, there will 
be a definite range of field strength throughout which the rays 
can pass through the system. Similarly, if the rays are not 
homogeneous to begin with, if we are dealing with the whole of 
the ^-rays from radium for example, there will be for every 
mao-netic field a finite range of velocities which the yS-rays may 
possess and still be able to pass through the system ; and if the 
size of the apertures is considerable compared to the radius of 
the path, and if the incident beam is of a fairly wide angle, this 
difference of velocities may be very considerable. We shall return 
to this point later. 

In addition to the broadening of the curve due to the finite 
width of his apertures, there was a second possible explanation of 
the shape of Schmidt's curves, namely that the rays from the 
radium E were not homogeneous. 

It was natural to assume that the ;8-rays from a single homo- 
creneous substance were homogeneous. In this case the fact that 
the maxima of the different curves always occurred for the same 
magnetic field, however much aluminium had been traversed, 
would prove that the rays kept their velocity unaltered during 
their passage through the fire. 

In a recent paper W. Wilson* has given considerable indirect 
evidence to show that the /8-rays from a single radio-active 
substance are not homogeneous, and in this case Schmidt's curves 
could only be explained on the assumption that there was a definite 
decrease in velocity as the rays passed through increasing thick- 
nesses of absorbing material. In brief, if the finite width of 
Schmidt's curves are due to the rays from the radium E having 
a definite range of velocities, as the faster rays are proportionately 
less absorbed than the slower rays, for any given thickness of 
aluminium, the maximum should gradually move out in the 
direction of the stronger magnetic fields, and the higher velocities, 
in the absence of any compensating change of velocity in the rays. 

From these considerations Wilson is able to deduce the change 
in velocity of /3-rays for different thicknesses of aluminium. He 
calculates thus that the velocity of certain of his rays changed 
from 2-78 x lO^" cms. per sec. to 2-69 x 10^" cms. per sec. in passing 
through 0-489 mm. of aluminium. 

It must not be forgotten, however, that the experiments of 

Schmidt, whichever way we regard them, do conclusively prove 

one important fact, namely that the /S-rays from a single radio- 

p,-coive siiuaw.ce are absorbed in such a way that the distribution 

* Pn.Roy. Soc. A, Vol. lxxxii. 1909, p. 612. 

Mr Crowther, On the Transmission of ^-rays. 445 

of velocities in the beam remains the same whatever the thickness 
of absorbing material traversed. 

Under these circumstances it was felt that some more direct 
experimental evidence on the point was desirable. 

The method employed consisted, briefly, in forming a beam of 
homogeneous /S-rays by means of the magnetic deflection method 
described above, and measuring the velocity of the rays so obtained 
by means of a second similar system of screens. Sheets of different 
absorbing materials could be placed in the path of the rays be- 
tween the two systems, and the velocity of the ra.ys before and 
after passing through the absorbing medium could be directly 

As has been already explained, the magnetic deflection method 
only gives a truly homogeneous beam of rays when the apertures 
are infinitely small. On the other hand only a limited quantity 
of /3-rays at the best can be radiated by any radio-active substance 
through a given area. The dimensions of the apparatus used, 
therefore, represent a compromise between these opposing factors. 

A further point has also to be considered, namely the possible 
scattering of the rays during their passage through the air. 
Recent experiments* show that if the path is at all long, the 
scattering of the rays by the air may be very considerable. It is 
possible that this effect may not seriously affect the purity of 
the rays transmitted, but in cases where it is desired to work 
with a nearly parallel pencil of rays (as in experiments to be 
described later) it is certainly of very considerable importance. It 
was decided, therefore, that the whole operation of deflecting the 
rays and forming them into a pencil should take place in vacuo. 

The form of apparatus finally decided upon is shown in section 
in fig. 2. The portion EFGH is placed between the poles of an 
electromagnet, so that the edges of the pole pieces lie along EF, 
and FQ. The tube DA projects from the magnetic field and is 
carefully screened by a thick block of soft iron, so as to cut off as 
far as possible any strong field from this part of the path. 
Windows of thin aluminium foil (-002 cm.) close the apertures at 
A and B. 

The radius of curvature of the path of the rays is 4 cms. and 
each of the apertures A, D, G, B is 0-5 cm. in diameter. The 
distance AD is 35 cms. and the depth of the box at right angles 
to the plane of the paper is 1-5 cms. The different apertures are 
bevelled, and the screens and sides of the box coated with 
aluminium foil to avoid as far as possible any secondary radiation. 
The apparatus could be exhausted by means of a water pump to 
a pressure of about 12 mm. of mercury, which was found to be 

* J. A. Crowther, Proo, Camb. Phil. Soc, YoJ. xv. 1909, p. 273. 
VOL. XV. PT. V. 29 

446 Ml' Groivther, On the Transmission of /3-rays. 

sufficiently low for all practical purposes. In experiments for 
which a parallel emergent beam was not necessary, the radium 
was placed at A. If, however, a parallel beam was desired (as in 
the experiments on the absorption of the rays to be described 
later) the apparatus was reversed and the radium placed at B. 

Two such chambers were made, and placed so that the window 
A of the one came directly opposite the window B of the other. 
The two magnetic fields were arranged so that rays of the proper 
velocity would be deflected round the two systems and emerge 
finall}'^ into an ionization chamber of the usual pattern. 

Fig. 2. 

The measurements of the ionization produced were made by 
means of the compensating method devised for experiments on the 
scattering of the /3-rays from uranium, and fully described in 
a previous paper*. In brief it consists in compensating the 
ionization current through the first chamber by an opposing 
ionization current from a second chamber connected to the 
same electroscope, in which the ionization can be varied, in a 

* J. A. Crowther, Proc. Roy. Soc. A, Vol. lxxx. p. 186. 

Mr Growther, On the Transmission of ^-rays. 447 

known manner, by means of a shutter sliding over a plate of 
uranium oxide. By placing a second small sample of radium 
near the compensator, the 7-ray leaks through the two chambers 
could be made to exactly neutralize each other, and thus the 
effect due to the /3-rays alone could be measured directly. 

Unfortunately the double system transmitted so very fev,^ 
y8-rays that it was not found possible to measure the effect on the 
velocity of interposing different screens between them. Enough, 
however, was transmitted to test the efficacy of the systems as a 
means of producing a beam of homogeneous rays. Keeping the 
first field constant and varying the second it was found that when 
the mean velocity of the rays transmitted through the first system 
was 2'77 X 10^" cms. per sec, the extreme values for the velocities 

of the rays, as measured by means of the second system, were 
2"75 X 10^" cms. per sec. and 2*79 x 10^" cms. per sec. The extreme 
velocities of the rays transmitted through one of the systems 
therefore do not differ by more than one per cent., plus or minus, 
from the mean value, and the system may be regarded therefore 
as giving a fairly homogeneous pencil of rays. 

In order to be able to work with absorbing screens it was 
necessary to make a further compromise in order to obtain a 
measurable effect. The first system was left unaltered so that 
a homogeneous pencil of rays of known velocity fell upon the 
screen. The distance AD in the second chamber was, however, 
reduced to 1 cm. The field across the first system in any given 
experiment was kept constant while that across the second was 


448 Mr Crowther, On the Transmission of ^-rays. 

varied. In this way curves connecting the intensity of the 
;8-radiation passing through the second system with the magnetic 
field both with and without an absorbing substance between the 
two systems could be obtained. The experiments were then 
repeated for different values of the first deflecting field, that is, for 
different velocities of the incident rays. 

Specimen curves, obtained with aluminium as the absorbing 
substance, are given in fig. 3. It will be seen that there is a con- 
siderable broadening of the curves even when there is no absorbing 
screen in the path of the rays. As the rays emerging from the 
first system have been shown to be very nearly homogeneous, this 
broadening is due to the greater latitude of path allowed by the 
second system owing to the shortening of the tube AD. It will 
be noticed that for aluminium this broadening of the curves is 
no greater with than without the absorbing layers. 

Fig. 3 shows the effect of interposing a sheet of aluminium 
0*47 mm. in thickness between the two systems, for two different 
velocities of the incident beam. The upper curve in each case is 
the curve obtained for the incident beam in the absence of the 
absorbing sheet. The ordinates represent the intensity of the rays 
passing through the two systems, as measured by the ionization 
produced ; the abscissae measure the magnetic field acting upon 
the second system. 

It will be seen that in each case the introduction of the 
absorbing sheet produces a very definite displacement of the curve 
in the direction of the smaller velocities. 

The actual figures deduced from these curves are given in 
Table I. 

Table I. 

Aluminium (0*47 mm.). 

Velocity of incident rays 

Velocity of emergent rays 

Percentage absorption of 
rays by the Aluminium 

2-735 X IQi" cm./sec. 
2-903 X IQi" cm./sec. 

2-690 X IQw cm. /sec. 
2-881 X 101" cm./sec. 


It is evident therefore that there is a small, but perceptible 
decrease in the velocity of the ^-rays as they pass through 
absorbing media. 

But though this small decrease in velocity accompanies absorp- 
tion, it is not sufficient to account for it. The third column in 

Mr Crowther, On the Transmission of ^-rays. 449 

the table gives the percentage of the incident rays absorbed in the 
aluminium sheet used ; and it will be seen that while 71 7o of the 
softer rays are absorbed in the aluminium screen used, the change 
of velocity is only of the order of about 2°/^. Allowing for the 
change in mass of the /S-corpuscles with change in velocity, which 
is fairly rapid at these high velocities, this corresponds to a loss 
of energy by the /3-rays of about 10°/^. Only a small portion 
of the whole absorption of the rays can therefore be due to 
this gradual decrease in velocity. For the main causes of absorp- 
tion we must seek elsewhere. However, as we shall see later, the 
gradual change in velocity of the rays may have a very appreciable 
effect in modifying the shape of the absorption curves. 

Glass screens gave very similar results to aluminium. Platinum 
on the other hand behaved quite differently. The curves obtained 
between the intensity of ionization and the strength of the second 
magnetic field were low, showed no decided maxima, and were 
very much broadened out in both directions, but particularly in 
the direction of the softer rays. On account of the very small 
amount of radiation transmitted for any given field it was not 
possible to determine the exact shape of the curves at all accu- 
rately. Some of the broadening may have been due to the rays 
on the whole emerging from the platinum more obliquely than 
from aluminium or glass, but it seems too great to be altogether 
explained on this assumption, and more probable that a homo- 
geneous pencil of /S-rays after passing through a platinum screen 
emerges with a very considerable range of velocities. This effect 
must be connected with some secondary radiation excited in the 
platinum. We shall return to this point later. 

§ 3. On the absorption of homogeneous l3-rays. 

The absorption of the yS-rays from a single radio-active sub- 
stance, such as uranium X, or one of the radium products, may be 
measured by interposing screens of absorbing material of different 
thicknesses between the radiating layer and an ionization chamber, 
and measuring the change in ionization produced. If the absorb- 
ing material is of low atomic weight the absorption curve can be 
represented accurately by the equation 

where / is the intensity of the radiation after passing through a 
thickness d of absorbing material, and A, is a constant. If the 
absorbing substance is of high atomic weight, there is a short 
initial steeper portion before the curve assumes the true expo- 
nential form. 

This law has been tested by many observers for practically all 

450 Mr Crowther, On the Transmission of ^-rays. 

substances emitting /S-rays over a very wide range of absorptions. 
N. R Campbell * found that for aluminium the exponential law- 
was certainly true to within 0"5 °/^ even when the rays had been 
reduced to one hundredth part of their initial intensity. 

W. Wilsonf, on the other hand, using a magnetic deflection 
method, found that the absorption of the " homogeneous " rays 
obtained by the magnetic deflection method certainly did not 
follow an exponential law, but a law which was practically linear. 
It is difficult to conceive any mechanism which would produce 
a linear law of absorption. Wilson, who worked principally with 
aluminium, notes that tin showed some departures from the linear 
law, but does not state either the nature or amount of these 
departures. It seems probable, therefore, that the linear law found 
for aluminium is only approximate and represents the balance of 
a variety of causes and conditions. 

For example the gradual change of velocity of the /S-rays in 
their passage through the aluminium would tend to transform an 
exponential law of absorption into a law which might approximate 
to a straight line. For consider a beam of homogeneous /8-rays of 
velocity v, and with a coefficient of absorption A,. If the exponen- 
tial law is accurately obeyed, and if the rays retain their original 
velocity, the curve connecting the logarithm of the intensity with 
the thickness of material traversed will be a straight line. As 
a matter of fact, however, after passing through a thickness d of 
material, the velocity of the rays has diminished to v', and the 
coefficient of absorption has increased to some value \'. Since X, 
varies rapidly with v (probably as the inverse fourth power of v) 
the change in A, will be quite perceptible even if the change in 
velocity is only small. Thus a change of velocity of only 2 °/^ 
such as was found to occur in 0*47 mm. aluminium might produce 
a change in \ of as much as 16 7o- Thus instead of the curve 
for log / being a straight line it would be some curve falling 
below this line, and its slope, which gives the value of X, becomes 
steeper and steeper as the thickness of material is increased. 
In fact we should have a curve similar in appearance to that 
given by Wilson for the absorption of homogeneous /3-rays by 
aluminium |. 

Prof. Sir J. J. Thomson § has very recently published a theory 
of the transmission of the /S-rays through matter, according to which 
the absorption of homogeneous rays should vary as (1 — e~*'^), where 
X is the thickness of material traversed, and ^ is a constant. This 
would give an absorption curve decreasing at first very slowly, 

* N. E. Campbell, Phil. Mag. Vol. xvii. 1909, p. 180. 

t W. Wilson, Proc. Boy. Soc. A, Vol. lxxxii. 1909, p. 612. 

X Wilson, loc. cit. p. 616. Fig. 4. 

§ Proc. Camb. Phil. Soc. Vol. xv. Part v. 1910. 

Mr Growther, On the Transmission of ^-rays. 451 

then much more rapidly, and finally tailing off into something not 
very distinguishable from the ordinary exponential law. 

The experiments now to be described have been made with a 
view to testing the various points briefly touched upon above; and 
to ascertain as exactly as possible the true shape of the absorption 
curve for some different substances. 

The apparatus used is sketched in fig. 4. The radium in a 
glass tube is placed at R in the centre of a large block of lead. 
A is one of the systems used for obtaining a homogeneous beam 
of /3-rays, fully described in the previous section of this paper 
and sketched in fig. 2. D is the ionization chamber into which 
the /3-rays pass. It is made of a copper hemisphere 12 cms. in 
diameter, with an inner electrode e of aluminium leaf, and a 
large opening dd, closed with thin aluminium leaf to admit the 
rays. The absorbing sheets can be introduced into the small 

Fig. 4. 

space left between the exit tube B and the window d, by means 
of a metal slide not shown in the figure. G is the shutter com- 
pensator described in detail in a previous paper, and TTan inclined 
gold leaf electroscope which differs from the original design in 
being only 1 cm. in depth. This variation has the advantage that 
it allows of the use of fairly high power objective and thus of a 
considerable degree of magnification in the reading microscope. 

G and D were charged to opposite potentials and their inner 
electrodes were connected through the key K to the electroscope 
W by wires passing through earthed metal tubes. These tubes 
were filled with sulphur and the key K was made small in order 
to reduce as much as possible the leakage from the electrodes 
through aiv ionized by 7-rays from the radium. 

452 Mr Growther, On the Transmission of ^-rays. 

The chief points in the method are therefore, briefly, as 
follows : 

(1) The homogeneous rays are produced by magnetic de- 
flection through a suitable system of apertures in a vacuum. 

(2) They fall upon the absorbing sheet normally, in a 
narrow and nearly parallel pencil. 

(3) The intensity is measured in an ionization chamber of 
such a form that, at whatever angle the rays emerge from the 
absorbing sheet, their length of path in the chamber is practically 
the same. 

Table II. 

Thickness x, in cms. 


logio II h 

xlog,,(l- III,) 

A luminiu7n : 





























Platinum : 


— _ 




- -00058 













It may be permissible to note in passing the advantages pos- 
sessed by the compensator method in experiments of this kind 
over the ordinary methods of timing the leaf over a given number 
of divisions. These are, in brief, 

(1) The large 7-ray leak through the ionization chamber is 
balanced by a similar leak through the compensator. In this way 
the effect due to the yQ-rays is measured directly, and not as 
a difference between two other large quantities. 

(2) The results are not affected by defects in the insu- 
lation, as is the case when a timing method is used. As a defect 
in the insulation only comes into play when the gold leaf system 
begins to charge up, it cannot affect the direction in which the 
leaf begins to move, and hence cannot affect the final balance. 
In a timing method, however, defective insulation will alter the 

Mr Growther, On the Transmission of ^-rays. 453 

rate of leak, and may cause considerable errors in the results. 
This point is of special importance in the present case, as it is 
always difficult to secure really good insulation in the presence of 
the 7-radiation from any considerable amount of radium. 

(3) The method is found to be very convenient in use, and 
capable of very considerable sensitiveness and accuracy. 

Experiments have been made so far on aluminium and 
platinum. The results obtained are given in Table II, and are 
represented graphically in figs. 5 and 6. The abscissae represent 


s-^ _^ 
































Fig. 5. 

in every case the thickness of the absorbing layer; the ordinates 
represent in the case of the full curves the corresponding values 
of ///o and in the case of the dotted curves the values of logio ///o . 
It will be seen that the two substances behave quite differently 
in their absorption of the /3-rays, and we will consider each 

The curve for aluminium at first descends very gradually and 
the quantity of rays absorbed increases very slowly with the thick- 
ness during the initial stages. On adding further thicknesses, 
however, the curve begins to descend more rapidly, and for part 
of its course becomes practically a straight line. For greater 


Mr Groiuthe7\ On the Transmission of 0-rays. 

thicknesses still the carve has another point of inflection; the 
absorption becomes less rapid, and the curve appears to become 
asymptotic to the axis of x. The small amount of rays trans- 
mitted by these thick sheets did not allow of any very exact 
determination of the shape of this part of the curve. The ex- 
periments seemed to indicate, however, that it did not depart 
widely from an exponential form. 

It will be seen that the curve thus obtained agrees well in 
its main outlines with the form of absorption curve predicted by 
Prof. Thomson's theory. It shows the same initial flat portion, 
the steeper middle portion and the final gradual tailing away. 






\ \ 

\ -v 

\ ^ 

\ V 











•005 cms. 

Fig. 6. 

More than a general resemblance could not well be expected. 
Prof Thomson's theory applies rigidly only to thin sheets of ab- 
sorbing media. Again the factor k in the equation 

is a function of the energy of the rays, and decreases as the energy 
is diminished. As the energy of the rays is continually diminish- 
ing during their passage through the aluminium, the value of k 
must also diminish with the thickness, and thus cause a de- 
parture from the predicted form. The last column of Table II 

Mr Growther, On the Transmission of ^-rays. 455 

gives the values of x\og{l —I/Io) which is proportional to k, and 
it will be seen that this product does diminish for the thicker sheets. 
On the whole the agreement between the experimental results 
and the theory is even closer than might have been expected, but 
it is evident that the phenomena of absorption are too complicated 
to afford any rigorous test of the theory. Experiments are now 
being made along other lines in order to determine this point. 

It will be seen that the curve differs from those given by 
Wilson in his paper, mainly in the initial portion. His curves 
show the final bending round along the a;-axis, though he seems 
inclined to ascribe it to experimental imperfections. It seems 
possible that the greater width of his apertures (1'2 cms. as com- 
pared with 0*5 cm. in these experiments) and the fact that the rays 
fell upon the absorbing sheets over a fairly considerable angle 
instead of in a nearly parallel pencil, caused a kind of general 
levelling out, and thus obscured the initial point of inflection of 
the curves. 

If now we turn to the absorption curves for platinum, we find 
an entirely different law of absorption. An examination of the 
dotted curve in fig. 6, representing the relation between log I/Iq 
and the thickness of the absorbing layer, will show that, except 
for a slight initial steepening, the curve may be represented by 
a straight line to an accuracy well within the probable errors of 
experiment. On the other hand the lower curve, giving the 
values of I/Iq, does not show the slightest approximation to a 
linear law. In fact the absorption of homogeneous /3-rays by 
platinum follows exactly the same law as the absorption by plati- 
num of the /S-rays from a single radio-active substance, that is it 
is exponential. 

The velocity of the /3-rays used in these experiments was 
2'77 X 10" cms, per second. The mean velocity of the /3-rays from 
uranium X, according to the measurements of H. W. Schmidt*, 
is 2"79 X 10" cm./sec. The homogeneous rays used in these 
experiments had therefore practically the same velocity as the 
rays used in previous experiments in the absorption of the ^-rays 
from uranium -j-. The value of X/p for platinum (where \ is the 
coefficient of absorption assuming the exponential law and p the 
density) found from the present experiments is 11*9; the value 
obtained with the uranium rays was 9*4 Considering the very 
different nature of the two experiments the agreement is fairly 

This result must undoubtedly be ascribed to some secondary 
radiation excited in the platinum by the incident rays. We have 
already seen that the rays emerging from platinum betray an 

* H. W. Schmidt, Le Radium, Vol. vi. 1909, p. 5. 
t J. A. Crowther, Phil. Mag. Vol. xii. 1906, p. 379. 

456 Mr Growther, On the Transmission of ^-rays. 

entirely different character to those emerging from aluminium 
when studied in a second magnetic field. While the latter are 
gradually reduced in velocity without any appreciable dispersion 
of their velocities about the mean, the former seem to possess 
a very considerable range of velocities. It may be noted that 
McClelland* has shown that the return /3-radiation from any 
radiator may be divided into two parts, which differ in their 
penetrating power and in their law of distribution. One has 
practicall}'' the same penetrating power as the primary /3-ra.js, 
and is probably purely scattered radiation; the second type is 
less penetrating and is probably a true secondary radiation. The 
former is the predominating factor in elements of low atomic 
weight such as aluminium, while the latter predominates in 
elements of high atomic weight such as lead or platinum. 

It seems, therefore, that the first stage in the absorption of a 
beam of homogeneous /S-rays by platinum is their transformation 
into secondary radiation (during the initial steeper portion of 
the curve). The absorption of these secondary rays in the further 
sheets of platinum then takes place according to an exponential 
law. The rapidity of this conversion, which seems to be complete 
in O'OOl cm. of platinum, is at first somewhat startling. It is, 
however, quite in accordance with previous experiments f on the 
scattering of the yS-rays from uranium, which may be regarded 
as showing that the distribution of the /S-rays in a sheet of gold 
reaches its final form in a thickness of little more than 0"0002 cm. 

It is interesting to notice that Sadler]: has very recently 
shown that the absorption of the secondary corpuscular radiation 
emitted from different radiators under the action of homogeneous 
secondary Rontgen rays is also absorbed according to an expo- 
nential law. 

We are thus led to the following result. When /3-rays are 
emitted by any substance, whether due to its own radio-active pro- 
perties, or excited by external radiation of a single definite type, 
the absorption of the rays emitted follows an exponential law. 
On the other hand the absorption of a homogeneous beam of 
yQ-rays by a substance such as aluminium which does not emit 
any large amount of true secondary radiation of its own, follows 
a law the precise nature of which remains to be determined, but 
which is certainly not exponential. 

If this is so, it follows, as Wilson has already suggested, that 
the rays from a single radio-active substance are absorbed accord- 
ing to an exponential law by virtue of some special distribution 
of velocities in the emergent beam. The results obtained in the 

* J. A. McClelland, Proc. Roy. Soc. A, Vol. lxxx. p. 501. 
t J. A. Crowther, Proc. Roy. Soc. A, Vol. lxxx. p. 187. 
:J: C. A. Sadler, Phil. Mag. March 1910. 

Mr Crowther, On the Transmission of /3-rays. 457 

present paper on the absorption by platinum, and the results of 
Sadler already alluded to, on the absorption of secondary cor- 
puscular radiation, show that if this is the case a similar distri- 
bution of velocities occurs also when secondary /8-rays are emitted 
under the influence either of homogeneous ^-rays or of homoge- 
neous Rontgen rays ; while the experiments of Schmidt, described 
in the earlier part of this paper, show that this distribution is 
not disturbed during the passage of the rays through very con- 
siderable thicknesses of absorbing material. 

A law so fundamental, applying equally to the emission of 
/3-rays under radio-active disintegrations, under the action of 
homogeneous /^-radiation, and under the action of homogeneous 
Eontgen rays, should be capable of some simple explanation in 
terms of the properties of the /3-rays and of the atom. Until 
further experiments have been performed however it seems pre- 
mature to frame any suggestion as to its cause, or even as to 
its precise nature. A knowledge of the true law of absorption 
of homogeneous rays would enable us to determine the initial 
distribution of velocities necessary to produce an exponential law 
of absorption, and Wilson, assuming that the law of absorption is 
linear, has calculated one such possible distribution. No theoretical 
evidence in favour of the distribution which he arrived at has yet 
been given, and the results of the present experiments seem to 
show that the "linear law" of absorption is only an approximation 
even for aluminium, and is probably the result of an interaction 
of the different causes producing and influencing the absorption 
rather than a fundamental law. 

One fact alone seems perfectly clear. The absorption of the 
yS-rays is a far more complicated phenomenon and is influenced 
by a far greater variety of causes than had previously been 
'imagined. It is only by disentangling the different phenomena 
involved and considering each of them separately that we shall 
arrive at any satisfactory idea as to the nature of the processes 


Experiments have been made on the velocity of a beam of 
homogeneous yS-rays before and after their passage through an 
absorbing medium. It was found that aluminium caused a small 
but perceptible diminution in velocity of the rays, without any 
appreciable disturbance of the homogeneity of the beam. On the 
other hand a homogeneous beam of /3-rays after passing through 
platinum emerged with a fairly wide range of velocities. 

458 Ifr Grotvther, On the Transmission of ^-rays. 

The absorption of a parallel pencil of homogeneous ;S-rays by 
aluminium and platinum has been determined. The absorption 
curve for aluminium is complicated, being neither "exponential" 
nor "linear." It approximates, however, to a form very recently 
suggested by Prof Sir J. J. Thomson. The absorption curve for 
platinum after a steeper initial portion is exponential. This 
result is assigned to secondary radiation. 

I take this opportunity of again expressing my best thanks to 
Prof Sir J. J. Thomson for much kindly interest and many 
helpful suggestions. 

Mr Lushy, Some Experiments on lonisation in Dried Air. 459 

Some Experiments on lonisation in Dried Air. By S. G. 
LusBY, Emmanuel College. (Communicated by Professor Sir 
J. J, Thomson.) 

[Read 14 March 1910.] 

(1) Introduction. In examining the physical properties of 
ions, one cannot help being struck by the important part which 
moisture plays in the determination of the coefficieKts which 
define these properties. 

For example, in moist air, the coefficient of diffusion of positive 
ions is -032, and that of negative ions is "035. If, however, the 
gas be dried, the coefficient for positive ions drops to '028, whilst 
in the case of negative ions there is a large increase to '043. 
Under certain conditions one can take advantage of this difference 
in the rates of diffusion between the two kinds of ions and com- 
municate a decided positive charge to the gas. 

Again, the velocities of ions in any gas are affected if the gas 
be allowed to retain any moisture ; for example, in moist air, the 
velocity of the positive ion under a potential gradient of 1 volt 
per centimetre is 1"37 centimetres per second, for the negative 
ion I'ol ; if the air be dried, the velocity of the positive ion is 
changed very slightly to 1*3 6, whilst that of the negative ion rises 
to 1-87. 

In both sets of measurements it is seen that the action of 
drying the gas is more pronounced in its effect on the negative 
ion, but it should be remembered that the positive ion is also 
affected, though in a lesser degree. Air does not show this latter 
modification very well — probably on account of its complex struc- 
ture — but in other gases, e.g. oxygen, hydrogen, and carbon dioxide, 
the effect is very marked, as is seen by studying any standard 
tables of coefficients. 

In condensation experiments this difference in the action of 
positive and negative ions is again noticeable ; each kind of ion has 
its own condensation point. The experiments of C. T. R. Wilson* 
have shown that when the ratio of expansion of a gas is 1'25, 
condensation occurs round negative ions, but not till the ratio is 
increased to 1*31 do the positive ions produce a condensation 
cloud. This suggests that the negative ions act more readily 
than the positive ions as nuclei for the condensation of water 

All these facts point to the conclusion that the negative ion is 
much more intimately connected with water vapour than the 
positive, and it was thought that if by some means an ionised gas 

* C. T. E. WUson, Phil. Trans. A, cxciii. 1899, p. 289. 

460 Mr Lushy, Some Experiments on 

could be thoroughly dried, then it should acquire a strong positive 
charge. The present paper gives an account of some experiments 
made to try and detect such an action in air. 

(2) Experimental conditions. The problem was first attacked 
directly. A stream of undried, unfiltered air was drawn through 
brass tubing by means of a water pump at an approximate rate of 
50 cubic centimetres per second. Near the end of the apparatus 
where the air entered was a roll of filter paper, 1 decimetre long, 
on which uranium oxide had been fixed by means of acetyl 
collodion : this served as the ionising agent. The ionised air then 
passed through a copper U-tube, which could be surrounded by 
liquid air, and then passed into a Faraday cylinder which was 
connected to a Wilson electroscope of ordinary type — a sensitive- 
ness of 60 divisions per volt being generally employed. In order 
to avoid diffusion effects as far as possible, the brass piping Avas 
chosen with a fairly large diameter (4 centimetres); the U-tube 
was necessarily smaller, being only 1'5 centimetres in diameter, 
and the total length immersed in liquid air was about 15 centi- 
metres. Liquid air was chosen as the drying agent in order to 
make the action as perfect as possible ; this method has the 
further advantage that it does not cause any mechanical filtering 
effect such as the use of calcium chloride or sulphuric pumice 
might produce. 

The experiment consisted in merely placing a cylinder of 
liquid air round the U-tube and testing the electroscope for 
charge. In no case could any charge be detected, even though 
the electroscope's sensitiveness was pushed as high as 80 divisions 
per volt ; special care was of course taken to render all insulations 

To further test the matter, the Faraday cylinder was replaced 
by a condenser of the type used by Zeleny and other workers with 
blast methods, so that the positive and negative charges could be 
measured separately and compared, by raising the outer wall of 
the condenser to an appropriate positive or negative potential 
whilst the inner electrode was connected to the electroscope. The 
diameter of the outer brass tube of the condenser was 4 centi- 
metres, that of the inner electrode 7 millimetres, and the total 
length was 15 centimetres; a potential was applied sufficient to 
drive on the inner electrode all ions whose mobilities exceeded 
1 centimetre per second. In order to avoid effects due to the 
charging up of the ebonite insulation, the air was made to enter 
and leave the condenser through earthed tubes. 

On measuring the positive and negative charges in the dried 
air blast, a surprising phenomenon manifested itself; the two 
charges were exactly equal, but were two or three times the 
corresponding quantities in the undried air. Results were variable 

lonisation in Dried Air. 461 

from day to day, but in no case was the ratio of increase less 
than 2. 

At first, it was thought that this effect might be due to the 
low temperature and dependent upon the metal of which the 
U-tube was composed. The copper tube was therefore replaced 
by a glass one of approximately the same section, and the experi- 
ment was repeated — but without any change in the result. 

The uranium oxide, the ionising agent, was then suspected ; 
if it gave off an active gas which condensed at the low temperature 
of liquid air, the results obtained might perhaps be explicable. 
Obviously this action could be eliminated by employing another 
ionising agent. The simplest that suggested itself was the natural 
ionisation of the air. It is well known that under normal con- 
ditions there is present in the atmosphere a quantity of radium 
emanation sufficient continually to produce small ions of both 
signs at the approximate rate of 30 per cubic centimetre. This 
gave a small but fairly constant source of ionisation to work on. 
Here again, the drying (or cooling) of the air almost trebled the 
ionisation, and the uranium was restored to its place. 

The only other possible causes for the phenomenon which 
suggested themselves were diffusion, recombination, and conversion 
of large ions into small ones. 

Diffusion was first tested. As was pointed out in the intro- 
ductory section of this paper, the coefficient of diffusion of negative 
ions in air is 50 7o greater than that of positive ions, and this 
should lead to an excess of positive ions, if conditions were such 
as to allow of such action. Although it seemed extremely unlikely 
that the large tubing used could account for the effect, the matter 
was tested directly. U -tubes of two different bores, one greater 
and one smaller than that originally used were inserted, but with- 
out any appreciable change in the result. 

The question of conversion of large ions into small ones 
promised to give an explanation of the phenomenon. These 
large ions, discovered by Langevin* in 1905, have a mobility 
of only 3 x 10~* centimetres per second and occur naturally in the 
atmosphere, there being normally about 2000 of each, sign in a 
cubic centimetre of air. The dimensions of the testing apparatus 
were such that only a negligibly small portion of them were 
caught. In a recently published paper, M. de Broglie-f" has shown 
that these large ions are produced by the combination of ordinary 
small ions (whose dimensions are of molecular order) with large 
" neutral centres," whose linear dimensions are 100 times that 
of a molecule, that is about the size of ultra-microscopic particles 
or particles suspended in colloidal solutions, namely about 10 fifi. 

* Langevin, C. R. cxl. 1905, p. 232. 
t de Broglie, Journ. de Phys. Dec. 1909. 

VOL. XV. PT. V. 30 

462 Mr Lusby, Some Experiments on 

M. de Broglie has further given a general method for detecting 
and controlling these nuclei. If by the action of drying, some of 
these large ions were broken up into a small charged portion and 
a large neutral system, the small portion would be caught by the 
testing condenser and give an effect of the nature observed. This 
type of analysis of the large ion, viz. into one charged and one 
neutral portion, is the only one admissible if we assume that the 
ion possesses only one electronic unit of charge and further assume 
that this unit is indivisible ; the latter supposition seems to 
be supported by experiment, but the former is as yet purely 

To test this theory, the air before entering the apparatus was 
deprived of all its ions — large and small — by passing through 
a long condenser charged to an appropriate potential. Small ions 
are quickly produced spontaneously, but it takes a fairly long time 
for these to combine with the neutral centres to form large ions. 
In some previous experiments carried out by the writer*, it was 
found that air thus deprived of large ions did not again acquire 
the normal number till after about 20 minutes ; de Broglie 
{loc. cit.) has investigated a similar effect, and states that it 
requires a considerable time for the large ions to attain their 
maximum number, but gives no exact figures. As the time 
required for the air to pass from the electrical filter to the U-tube 
is at the most only 5 seconds, one seems justified in concluding 
that no appreciable reproduction of large ions occurs in this interval. 
On trying the above experiment, it was found that the result was 
quite independent of the large ions present in the air. 

There now remained only the question of recombination, which 
however did not promise to give a solution of the problem ; for 
recent work by Erikson-j- has shown that the coefficient of recom- 
bination increases as the temperature decreases, which obviously 
would give an effect entirely opposed to that observed. It is true 
that the coefficient thus found was under conditions of constant 
density, whereas in the present investigation conditions of constant 
pressure obtained. Still one could roughly suit the constant 
density coefficient thus found to the present case (where the 
pressure at any temperature would be higher) by superposing on 
it conditions of increased pressure. Now, according to M^Clung|, 
the coefficient of recombination is independent of pressure between 
the limits of 0"1 and 3 atmospheres ; whilst Langevin § showed 
that below these limits the coefficient decreases rapidly as the 
pressure is lowered. Thus an increase of pressure would in the 

* Lusby, Journ. Roy. Soc. N. S. W. June 1909. 
t Erikson, Phil. Mag. Aug. 1909. 
+ M«Clung, Phil. Mag. March 1902. 
§ Langevin, C. R. cxxxiv. 1902, p. 646. 

lonisation in Dried Air. 463 

former case not affect Erikson's coefficient at any temperature and 
in the latter case would increase it. In either case, the effect 
of temperature on recombination would give a result quite the 
opposite to that observed. Still, in order to verify this theory, 
the position of the ionising agent was altered, and it was placed 
between the U-tube and the testing condenser. Obviously, if 
recombination were causing the phenomenon, the current received 
by the electroscope would depend on the distance between the 
uranium and the testing condenser. The result was surprising; 
the ionisation in the dried air was increased to 10 times that in 
ordinary air, instead of only twice, as before. This seemed to 
point to the fact that reduced recombination occurred in the dried 
air, although I am not aware that any previous experimenter 
ever suspected or allowed for this action. To make sure of the 
point, the air before entering the apparatus was passed first 
through a tube 3 decimetres long, containing calcium chloride, 
and then through another tube 4 decimetres long, containing 
pumice, which had previously been treated with sulphuric acid 
in the ordinary way. On immersing the U-tube in liquid air as 
before the ionisation was still increased tenfold, and the negative 
action of water vapour on recombination confirmed. 

The only other thing that remained to be tried was the effect 
of dust. All early experimenters on recombination found that, in 
order to obtain consistent results, dust must be carefully excluded 
from the gas experimented on — a result clearly illustrated by 
Owens'* experiments with tobacco smoke. Although it seemed 
extremely improbable that drying (or cooling) a gas could remove 
its dust particles, still the result of filtering the air was tried. 
At first, only a decimetre of cotton wool was used, with the result 
that, on drying the air as before, the increase in ionisation was 
only about 100 7^ ; when the length of cotton wool was increased 
to 5 decimetres the phenomenon vanished altogether, and was 
therefore due solely to recombination. 

(3) Discussion of Results. The negative result obtained in 
the primary investigation, namely the absence of any preponder- 
ance of charge of one sign in dried air, is certainly disappointing. 
As was pointed out earlier, practically all the known properties 
of ions are modified by water vapour, such modification being 
more pronounced in the case of negative ions ; still one must not 
forget that the positive ion is also affected by moisture, though to 
a lesser degree. It may be objected that the effect sought for is 
masked by the recombination effect ; but that is not so, for in the 
first method employed the electroscope was quite sensitive enough 
to easily record a 5 7o difference between the two charges. Further, 

* Owens, Phil. Mag. Oct. 1899. 


464 Mr Lusby, Some Experiments on lonisation in Dried Air. 

in the very last experiment carried out — namely, that with filtered 
air — the effect of drying alone was tested, and neither the positive 
nor the negative charge was affected. This result shows that 
either the ions go through the U-tube intact, or else they drop 
their water molecules and pass on; and their mobilities in the 
latter case being presumably those they would possess in dry air, 
they are still caught by the testing condenser. 

The secondary effect, accidentally discovered, is in some ways 
more interesting than the main result, on account of the light 
which it seems to throw on the nature of the large neutral centres 
in the air, investigated recently by de Broglie {loc. cit). In the 
atmosphere there are normally present three types of bodies which 
are of importance in an ionisation theory, viz. small ions, neutral 
centres, and large ions, the latter being a combination product 
of the two former. When a gas is in statistical equilibrium, some 
of the small ions are constantly combining with small ions of 
opposite sign, others combine with neutral nuclei to form large 
ions, and a proportion of these large ions combine with large ions 
of opposite sign. Here two main coefficients of recombination 
have to be considered, that of small ion with small ion, and that 
of small ion with large ion. Now, other things being equal, the 
coefficient of recombination between two ions depends on the sum 
of their mobilities, hence the former coefficient is approximately 
twice the latter. But as the large ions outnumber the small ones 
by 50 to 1, the chief factor in recombination is the large ion ; 
or — to go back one step — the neutral centre. Hence anything 
that removes these large nuclei will tend to reduce recombination ; 
this is the present-day method of accounting for the action of 
so-called "dust." As to what happens to these nuclei at the 
temperature of liquid air one can only speculate. They must 
either be deposited in the U-tube or else dissociate into smaller 
bodies, whose chances of combining with a small ion are rare. 

de Broglie {loc. cit.) states that high temperatures break up 
the nuclei ; it is reasonable to suppose that a low temperature 
could do the same. If we supposed them to consist partly of solid 
and partly of gaseous matter, then the great difference in the 
coefficients of expansion of the different constituents could con- 
ceivably break up the complex system at a low temperature, on 
the same principle that daiup rocks crack in cold weather. It is 
important to note that water plays no part in this action ; the 
effect occurs equally well in dry or damp air. Whatever may be 
the composition of the neutral centre (and therefore of the large 
ion) evidently water is not present to any large extent. 

In conclusion, I wish to thank Prof Sir J. J. Thomson for his 
valuable suggestions and kindly interest during these experi- 

Professor Thomson, On the Scattering etc. 465 

On the Scattering of rapidly moving Electrified Particles. By 
Sir J. J. Thomson, Cavendish Professor of Experimental Physics. 

[Read 21 February, 1910.] 

When rapidly moving electrified particles pass through matter, 
each particle as it passes through an atom of the substance, or 
perhaps even when it passes close to such an atom, is deflected. 
The amount of the deflection will vary with the way the par- 
ticle strikes the atom ; there will, however, be a mean value 
for the deflection produced by an atom on the direction of 
motion of a particle passing through it, and when we are con- 
sidering only the effects produced by large collections of particles 
we may suppose that the path of each particle suffers the mean 
deflection. The direction of this deflection is quite arbitrary. 
Let us consider now the case when a large number of particles 
pass through a large number of atoms and consider what would 
be the average deflection of the particles after they have passed 
through n atoms. Since the direction of the deflections are quite 
arbitrary, it is evident that the problem is the same as that of 
finding the average value of the resultant of n displacements of 
arbitrary phase and of constant amplitude 6; if ^ is the average 
deflection of a particle passing through an atom. This average 
value is known (see Lord Rayleigh, Theory of Sound, 2nd Edition, 
Vol. I, p. 35) to be \/n . 9. Thus if the electrified particles are 
corpuscles moving normally through a plate of thickness t, then 
if there are N atoms per unit volume of the plate, and if h is the 
radius of an atom, the number of atoms traversed by a particle 
on its journey through the plate is JSfirb^t, and hence the mean 
value of the deflection experienced by a particle when passing 
through the plate is '^Nirh-t . 6. 

This supposes that the particle is not bent so much in passing 
through the plate that the length of its path is materially 
different from t. 

We shall now proceed to calculate the value of 9. 

Regarding the atom as consisting of Nq negative corpuscles, 
accompanied by an equal quantity of positive electricity, the 
deflection a negatively electrified particle experiences when 
passing through the atom arises from two causes. (1) The 
repulsion of the corpuscles distributed through the atom, and 
(2) the attraction of the positive electricity in the atom. 

The amount of deflection due to (2) will depend upon whether 
the positive electricity is uniformly distributed through the atom, 

466 Professor Thomson, Oii the Scattering of 

or whether it is supposed to be divided into equal units, each 
occupying a finite volume probably much greater than the volume 
occupied by a corpuscle. 

We shall calculate the deflections due to the negative and 
positive charges separately. Let us take that due to the cor- 
puscles first. We can show easily by the theory of forces varying 
inversely as the square of the distance that when the moving 
particle is travelling so rapidly that its deflection is small, this 
deflection is equal to 

2f_ 1 
mV^ x' 

when V is the velocity of the particle, e its charge, m its mass, 
and X the perpendicular let fall from the corpuscle on the direction 
of motion of the particle. Thus the mean value of the deflection 
pi'oduced by the corpuscles which are within a distance a of the 
line of motion of the particle, supposing the corpuscle uniformly 
distributed is 

4e- 1 

mV- a 

Now if the length of the path of the particle in the atom is I, 
the number of collisions between the particle and the corpuscles 
within a distance a from its path is, when the corpuscles are 
uniformly distributed, niraH, when n is the number of corpuscles 
per unit volume of the atom ; hence by the theory of probability 
the average value of the total deflection of the corpuscle when 
passing through the atom is 

4e2 1 

mv^ a 

_ 4e2 

~ — n Nmrl, 
mv- ' 

Now if b is the radius of the atom, the mean value of \/l is 
I '\/2b. Hence 6-^ the mean deflection of the particle due to the 
corpuscles in the atom is given by the equation 

01 = -^ -^ V?i7r6 
5 mv^ ^ 

16_e^l /3N, 
5 mv'^ 6 V 2 ' 

where Nq is the number of corpuscles in the atom. 

Let us now take the case of the positive electricity, let ^i be 
the average deflection when the positive electricity amounting 

rapidly moving Electrified Particles. 467 

to NqC is supposed to be uniformly distributed through the sphere 
of radius h, then it is easy to prove that when ^j is small it is 
given by the equation 

, e'' 
^ mv 4 

When the positive electricity is made up of definite units 6^ 
the mean deflection due to these is given by the equation 

16 e^ 1 /2>N. 

where o- is the ratio of the volume occupied by the positive 
electricity to the volume of the atom. 

The mean deflection Q due to both negative and positive 
particles will be 

{e,^-^<^^f- or (^,^ + <^M 

according as we take the first or second hypothesis. 

The average deflection when passing through a thin plate 
whose thickness is t is 's/Nirh^t . 6, and substituting the values 
of 6, we find for this quantity 

or — - 




1^ (A) 

according as we suppose the positive electricity to be uniformly 
distributed through the atom or done up into separate units. 

As these expressions contain no unknown factors beyond No, 
the number of corpuscles in an atom, they indicate that ex- 
periments on the scattering of light by very thin plates afford 
a simple method of determining the number of corpuscles in the 
atom. In making these experiments it is necessary to remember 
that we have supposed the deflection small so that the length 
of path was equal to the thickness of the plate, and secondly we 
have supposed that the velocity remained unchanged ; as the 
deflection varies rapidly with the velocity this condition is im- 
portant, and it is the more so because the expressions for the 
change in the velocity of the corpuscle produced by collision with 
an atom are (see Discharge of Electricity tlwough Gases, 2nd 
Edition, p. 378) much more complicated than those for the de- 
flection, they involve other quantities besides the number of 
corpuscles in the atom and thus are not suitable for measuring 
that quantity. I am not aware of any experiments made quite 

468 Professor Thomson, On the Scattering of 

under the conditions contemplated in equations A, but such are 
now being made by Mr Crowther at the Cavendish Laboratory. 
The observations we have are, however, sufficient to show that 
Nq is of the same order as the atomic weight of the atom. 

We see from equations A that when the deflection is small 
the thickness of the layer of a substance required to produce 
a given deflection varies as 

m-V 1 (385 7r_^ ^ I 
e' NNo 1 25 ^16 "I 

■i^F^ 1 385. 


e^ NN, 25 

according as the positive electricity is uniformly distributed 
through the atom or collected into separate units. We can 
show that this result is true even when the deflection is not 
small provided the velocity of the particles remains unaltered. 

For let f{z, ^) x 6 he the fraction of the particles which at a 
distance z from the point of projection, measured parallel to the 
original direction of projection, have a deflection cf), where <^ is 
between md and {771 + 1) 6. 

Let A, be the mean free path of a particle, then f(z + X cos (p, md) 
will be got from those particles which at a distance z had 
deflections {m — l)6 or {m + \)6; each of these particles will 
have made another collision, and if they are equally likely to 
be deflected in one direction as the opposite, we see that 

f{z + \eo^^,me)^\f{z,{m-l)e] + \f[zXm+l)e], 

(compare Lord Rayleigh, Theory of Sound, vol. i. p. 35). 
Expanding by Taylor's Theorem we get 


'^^^-^-'^ d^^ 


cos (j) ^^ 

df{z,cf>) ,d\f(z,<t>) 
dz '^ d^^ 

hence if we put 

e-'z , 

we have 

, df - d^f 

an equation which determines / as a function of / and 0. Since 
the same value of z' will give the same value of ^, it follows that 

rapidly moving Electrified Particles. 469 

layers of different substances will produce the same deflection if 

their thicknesses are proportional to Xjff^ ; since X = -^ ,^ we see 

that this implies that the results expressed by equations B are 
true even when the deflections are not small. 

In the preceding investigation we have supposed that the 
angular deflections were all in one plane, the differential equation 
satisfied hy f{z,<l>) when the deflections take place in any plane 
may be found as follows : 

As before the particles for which z = z ■\-\cos^, and (f>=4>i 
must have come from the particles determined by z and (f)o where 

cos ^1 = cos ^2 cos 6 + sin ^2 sin 6 cos'^jr, (1) 

i/r is the angle which the plane in which the deflection 
takes place makes with the plane through the original direction 
of the particle and its direction just before it experiences the 
deflection 6. As all directions of yjr are equally probable the 
probability of -yjr being between -vlr and yjr + dy^r is dy^jzir. 

f{z + \ cos 0, <^i) =j-^f(z, (f),), 

by Taylor's Theorem, the right-hand side is equal to 

+ i;|^W„"^(*-^'^' (2). 

From equation (1) we get 

4>2 — <f>i— ^ cos ^jr — ^d^ cot (pi sin^ \/r, 
substituting this value of ^2 — <f>i in equation (2) we get 


4Xd/_ 1_^ 1 d-^f 

0^ dz sin <f) d<f) cos (f) dcj)^ ' 

or if cos (}> = t, the equation may be written 

d' dz~ t dt^' 
or with the same notation as before, 

^ df ^l-t^ d?f 
dz t df ' 

470 Professor Thomson, On the Scattering of 

The conclusions drawn when the deflections were all in one 
plane may thus be extended to the more general case. 

Although as yet we have no experiments in which the 
arrangements have been such as to admit of an accurate applica- 
tion of the formulae obtained in this paper, we have data by 
which we can calculate the order of the quantity N^ the number 
of corpuscles in an atom. 

Let us find the path of a particle which moves so that its 
deflection is equal to the average deflection for the number of 
collisions made by the particle, i.e. if ^ is the angle through 
which the direction of the particle is deflected, n the number of 
collisions made by the particle 

</) = Vn ^. 

If s is the length of path travelled by the particle, \ the 
mean free path n = s/\ and </>^ = sd'^/\. 

If cc is the distance, measured parallel to the direction of 
projection, travelled by the particle 


X . <^- 
or since s = ^^ , 

dx = -^^ cos ^,(f).d^, 


or a; = -^ {<^ sin ^ + cos (p — 1], 

so that when = 7r/2, or the particle is bent at right angles to 
the direction of projection, 

when X is greater than this the particle will begin to travel back 
again, hence this value of x must be comparable with the distance 
at which the number of particles crossing a plane at right angles 
to the direction of projection is reduced to one half of those 

Substituting the value of X/^^ previously found we get 


384i\^„ -^2 


71 rv- 
x= (tt — 2) -Tw- 

if we take the second of equations (B), 

putting ejm = 51 x 10", e = 5 x lO"", v = 10", iV - 2 x 3 x lO^", 

rapidly moving Electrified Particles. 471 

we find that for any gas at atmospheric pressure when the 
particles have this velocity 

a; = (tt — 2) X roughly. 


Becker found that cathode rays of about this velocity travel 
through about '5 cm. of oxygen before the number moving 
forwards is reduced to \. Putting a3 = | we get for Nq about 50, 
if the number of corpuscles were equal to the atomic weight 
Nq would be equal to 16. Thus these experiments show that the 
number of corpuscles in the atom is of the same order as the 
atomic weight ; we must, however, wait for experiments made on 
different lines before we can determine the exact relation between 
the number of corpuscles and the atomic weight. 

472 Mr Dixon, Jacobi's double-residue theorem 

Jacobi's double-residue theorem in relation to the theory of 
point-groups. By A. C. Dixon, Sc.D,, F.R.S., Trinity College. 

[Read 23 Mai/, 1910.] 

In this paper I have shewn how Jacobi's theorem leads 
directly to the chief general propositions of the theory of point- 
groups in a plane, and have also given a discussion of a converse 
theorem. No account has been taken of coincidences among the 
points of a group. 

1. Jacobi's theorem is as follows. Let u, v, w be three 
polynomials in two variables oc, y, of degrees m, n, m-\-n — S 

respectively, and let J be the Jacobian ^^-^ — ^ . If the mn points 

o [x, y) 

of intersection of the curves w = 0, v = are all distinct and at 
finite distance from the origin, and are denoted by {x^, y^) (r=l, 
2 . . . mn), then 


^ w(Xr, yr)/JiXr, yr) = (1). 


(See for instance Netto, Vorlesungen ilber Algebra, vol. ii, 
pp. 165—173.) 

The following proof is a modification of one given by Netto, 
after Kronecker. 

If w is an arbitrary polynomial of degree m + n— 3, it contains 
I (m + w — 1) (m + ?i— 2) arbitrary coefficients, and if w is re- 
stricted by being supposed to vanish at (x^, yr) {r=l,, 
this number of coefficients is brought down to 

^ {m + n — 1) (m + n— 2) — mn 

or ^(m- 1) (m - 2) -\- ^(n -1) (n~2) -1 

if all the conditions w (x^, yr) = 0, to be satisfied by those co- 
efficients, are independent, that is, unless there is some relation 

S Ar W {Xr, yr) = 

satisfied by all polynomials w of the degree m + n— S. 

Now if <j), yfr are any polynomials of the degrees n — S,m — S, 

Ucfi + V^lr 

is of the degree m + n — S and vanishes at the mn points, and 
contains ^ (m—l) (m — 2) + ^ (n — 1) (n — 2) arbitrary coefficients, 
namely those in ^ and yjr, these being all effective unless for some 
set of coefficients u(fi + v-yjr is identically zero, that is, unless u, v 

in relation to the theory of point-groups. 473 

have a common factor*; which is contrary to the supposition that 
the curves m = 0, v = meet in mn isolated points. 
There must then be a relation of the form 


S Ar w{Xr,yr) = (2), 

r = 1 

satisfied by an arbitrary polynomial w of degree m + n — 3. 

The coefficients A can be found by constructing certain 
particular polynomials by Kronecker's method. 

* There is a slight difference in the argument at this point when the number of 
variables is greater than two. Suppose for instance there to be three variables 
xi, X2, X3 and ui, u^, Uz to be polynomials of degrees mx, m2, m^ and lo to be of 
degree mj + wi2 + WI3 - 4, so that Jacobi's theorem becomes 

/ 0{Xi, X2, Xz) 

It is possible to have polynomials 4,-^, (p2, ^3 of degrees ni2 + m3-4, ms + m^-i, 
mi + m.2-i, such that 

i«X^l + U2<t>2 + U3<p3 = 0. 

Using a bar to distinguish the terms of highest degree we have 

Wj^l + U2<p2 + «303 = 0, 

a homogeneous relation. It is supposed that the surfaces ui, 112, u^ have no 
common point at infinity, and hence when W2 = and 2*3 = 0, mi cannot vanish, so 
that ^1 = 0. Thus by Nother's theorem (§ 7 below) 

<P\ = W2r/'3 - U31P2, 

where \p2 . fs are of degrees ni2 - 4, ma - 4 and homogeneous. It follows that 

W2 (^2 + "1^3) + M3 (^3 - u-^i) = 0, 
and that ^2 = '/'1W3 - ^■^i , 

03 = ^2"l-'/'lW2. 

where \j/i is homogeneous of degree nii- 4. 
Hence in the identity 

"101 + "202 + "303 = 0, 

01 ) 02 » 03 may be replaced by the polynomials of lower degrees, 

01 - W2'/'3 + «3^2 . 02 - W3\^l + "l 03 , 03 " "l 02 + "201 , 

and the degrees of these may be lowered similarly until we arrive at the result 

01 = "203 -"302 J 02 = "301 -"103. 03 = "l 02 " "201 , 

where 0i, 02, 03 are of the degrees mj - 4, w(2 - 4, m^ - 4. 

Thus if 01, 02, 03 are arbitrary polynomials of their degrees the effective number 
of arbitrary coefficients in 

"101 + "202 + "303 

is the number of coefficients in <pi, 02, 03 diminished by the number in 0i, 02, 03, 
that is, 

^[(m2 + 7ft3-l) (m2 + m3-2)(m2 + ni3-3) + (?n3 + mi-l)(»n3 + mi-2)(m3 + mi-3) 
+ {mi + 7«2 - 1) (toi + m2 - 2) {mi + m2 - 3) - (mi - 1) (mi - 2) (mi - 3) 
- (m2 - 1) (m2 - 2) (m2 - 3) - (mg - 1) (mg - 2) (mg - 3)], 
or |(mi + m2 + m3-l) (mi + ??i2 + m3 - 2) (mi + m2 + wi3-3) -mim2m3 + l. 

474 il/r Dixon, Jacohi's double-residue theorem 

Since ccPyi - ^PtjI = (xv - ^p) yi + {if - 7]i) p, the sum of two 
terms Avhich contain the factors x — ^, y — t] respectively, we have, 
taking the terms of u separately, 

u (x, y)-u (e 7?)= U, {x-^)+U, (y-v) (3) 

where Ui, U« are polynomials of degree m — 1 in x, y, f, t), and 
when x=^ and y = r], Ui, C/g are equal to the derivatives Ui, u^- 

v(a^,y)-v(^,v)=V,(x-^)+V,(y-v) (4) 

where F^, F^ are of the degiee n— 1 in x, y, ^, rj and reduce to 
the derivatives ■Vj, Vo when x = ^, y = 1]. 

Let Ui V.,— t/g Fj = A (x, y, ^, ?;), then, by substituting 

^r, y,-, ^s, Vs for X, y, f, t; in (8) (4) 

we find H^ {xr, yr, Xg, yg) — 0, when r=f^s, while ii =J {x,., y,), 
when r = s. J{xr,yr) is not zero since the curves t< = 0, v = 
have only isolated intersections. 

Now A {x, y, Xg, ys) — A (x, y, xt, yt) is of the degree m + n — '^ 
only in x, y, the terms of degree m + ?i — 2 destroying each other. 


S A,. {A {xr, yr, Xg, ys) - A (x,., y,., Xt, yt)] = 0, 

that is AgJ(xs, y^) - AtJ(xt, yt) = 0. 

This holds for all suffixes s, t and therefore the relation (2) is 

tw(x.,., yr)/J(i^r,yr) = (1), 

which is Jacobi's theorem. 

2. It follows directly that if w vanishes at mn — 1 of the 
intersections of u, v it vanishes at all, or that any curve of degree 
(?n + n — 3) through mn — 1 of the intersections of two curves of 
degrees m, n passes through all their intersections. 

Again, let (f) be an r'" (r <m + n — 8) vanishing at the first 
mn — a of the intersections, and -yjr an arbitrary (m + n — r — 3)^*^. 
We may put ^i/r for w and thus we have 


t 4> {Xr , 2/,.) y^r {Xr ,yr)/J (^r , ^r) = 0, 


an equation which includes 

^ (m + n—r—l)(m+n — r—2) equations, 
linear in (f) {x^, y^) (r = mn — a + 1, ... mn), 

and therefore gives ^ (x.,., yr) = for all these values of r if 
a = ^ (m + n — r — 1) {in + n — r — 2), 

in relation to the theory of point-groups. 475 

and if all these a equations are independent, that is, unless for 
some set of coefficients 

i/r [xr, 2/r) = (r = niu — « + 1, ... mu). 

This is the theorem of Cayley and Bacharach, that a curve of 
degree r{<m+n — 2), which passes through all but 

^(m + n — r — l)(m + n — r—2) 

of the mn intersections of two curves of degrees m, n, passes 
through the excepted intersections also unless these excepted 
points lie on a curve of degree m + n — r — S. There is no ex- 
ception when r = m + n — S. 

Similarly in three dimensions, a surface of degree ni + n+p — 4!, 
which passes through all but one of the intersections of three 
surfaces of degrees m, ?i, p, passes through all, and a surface of 
lower degree r must pass through all the intersections if it 
passes through all but 

^(m + n + p —1 — 1) (m + n + p — r— 2)(m+ n +p — r — 3), 

unless these excepted points lie on a surface of degree 

m + n + p — 1 — 4. 

Bacharach has further noticed that the lowest value of /8, 
such that an r''^ curve can pass through mn — /8 of the inter- 
section of u, V, say A, without passing through the rest, say B, 
is m + n — r—1, and that in such a case the points B are collinear. 

For if i/r is any (m + n — r — 3)'° we have 


the summation being over the /S points B, and thus any i^ 
through all but one of these passes through the other. If 

^ = m -\- n — 1 —